Answers
This given series [tex]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n!}[/tex] diverges.
What is the ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given a series, [tex]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n!}[/tex] we need to see if the series converges or not.
the ratio test will fail if [tex]\displaystyle \lim_{n\to \infty} \left |\frac{a_{n+1}}{a_n} \right | =1[/tex]. Otherwise, the series converges absolutely if [tex]\displaystyle \lim_{n\to \infty} \left |\frac{a_{n+1}}{a_n} \right | < 1[/tex] and diverges if [tex]\displaystyle \lim_{n\to \infty} \left |\frac{a_{n+1}}{a_n} \right | > 1[/tex]
Testing for the series [tex]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n!}\\[/tex],
=> [tex]\displaystyle \lim_{n\to \infty} \left |\frac{a_{n+1}}{a_n} \right |[/tex]
=> [tex]\displaystyle \lim_{n\to \infty} \left |\frac{(n+1)!}{n!} \right | \\[/tex]
=> [tex]\lim_{n \to \infty} (n + 1)[/tex]
This value will always be greater than 1 for any positive value of n.
Therefore, This given series [tex]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n!}[/tex] does not converge.
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Related Questions
Factorise fully 20xy - 54
Plss answer
Answers
So the answer is,
2( 10xy - 27 )
The factorisation of 20xy - 54 can be expressed as 2( 10xy - 27 ).
What is factorisation?The concept here is the factorisation . The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics.
A number or other mathematical object is factorized or factored when it is written as the product of numerous factors, typically smaller or simpler things of the same kind.
We were given, 20xy - 54, we can see that that factor of 2 is common for both 20xy and 54.
Then we can factorize as 2( 10xy - 27 ).
2( 10xy - 27 )
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A cylindrical pottery vase has a diameter of 4.3 inches and a height of 11 inches. What is the surface area of the vase? Use the formula SA= B+ Ph, since the vase has a bottom but no top. Use 3.14 for TT and round to the nearest tenth of a square inch.
Answers
Answer: To find the surface area of the cylindrical vase, we can use the formula:
SA = B + Ph
Where B is the area of the base (the circular top of the vase), P is the perimeter of the circular top of the vase, and h is the height of the vase.
We know that the diameter of the vase is 4.3 inches and the height of the vase is 11 inches. To find the radius of the base, we can divide the diameter by 2:
r = 4.3 inches / 2 = 2.15 inches
The area of the base is given by πr², so:
B = πr² = π * 2.15² = 14.65 square inches
To find the perimeter of the circular top we can use 2πr:
P = 2πr = 2 * 3.14 * 2.15 = 13.64 inches
Now we can substitute these values into the formula:
SA = B + Ph = 14.65 + 13.64 * 11 = 260.04 square inches
Rounded to the nearest tenth, the surface area of the vase is 260.0 square inches.
Step-by-step explanation:
(Show your work please) Rewrite in simplest rational exponent form square root of x times the fourth root of x. Show each step of your process.Rewrite in simplest rational exponent form square root x times 4 square root x
Answers
By applying the exponential properties, it can be concluded that the simplest rational exponent is [tex]x^{\frac{3}{4} }[/tex]
Exponential is a repeated multiplication method with the same number, which is notated in the form aⁿ, where a is called the base and n is the exponent or power.
Some properties of exponent:
[tex]a^{x}[/tex] x [tex]a^{y}[/tex] = [tex]a^{x+y}[/tex]
[tex]a^{x}[/tex] : [tex]a^{y}[/tex] = [tex]a^{x-y}[/tex]
[tex](a^{x}) ^{y}[/tex] = [tex]a^{xy}[/tex]
[tex](\frac{a}{b} )^{x}[/tex] = [tex]\frac{a^{x} }{b^{x} }[/tex]
a⁰ = 1
a⁻ˣ = 1 / aˣ
In mathematics, a radical is described as [tex]\sqrt[n]{x}[/tex], where n is a positive integer ≥ 1 and x is a real number. Then n is called the index of the radical, x is the radicand, and the symbol √ is the radical.
The radical can be written as a rational exponent as follows:
[tex]\sqrt[n]{x} = x^{\frac{1}{n} }[/tex] or [tex]\sqrt[n]{x^{m} } = x^{\frac{m}{n} }[/tex]
From the problem, we can denote the expression as follows:
square root of x = √x
the fourth root of x = ⁴√x
The product of the two expressions will be:
(√x) x (⁴√x) = [tex]x^{\frac{1}{2}}[/tex] x [tex]x^{\frac{1}{4} }[/tex]
= [tex]x^{\frac{3}{4} }[/tex]
Thus the simplest rational exponent is [tex]x^{\frac{3}{4} }[/tex]
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How did World War I affect fiction writing?
Answers
Answer:
Step-by-step explanation:
wwI effected fiction writing in many ways such as _________________.
Answer:
The First World War evoked a surge in literary output, which included poems, novels and drama. Whilst the poetry of Siegfried Sassoon, Rupert Brooke and Wilfred Owen immediately springs to mind, works by by Ivor Gurney, Edward Thomas, Charles Sorley, David Jones and Isaac Rosenberg are also widely anthologised.
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True or False: In testing hypotheses, the researcher initially assumes that the alternative hypothesis is true and uses the sample data to reject it.
Answers
In testing hypotheses, the researcher initially assumes that the alternative hypothesis is true and uses the sample data to reject it. This statement is False.
Hypothesis testing is an inferential procedure that uses data from a sample to draw a general conclusion about a population. It is a formal approach and a statistical method that uses sample data to evaluate hypotheses about a population. When interpreting a research question and statistical results, a natural question arises as to whether the finding could have occurred by chance. Hypothesis testing is a statistical procedure for testing whether chance (random events) is a reasonable explanation of an experimental finding.
In hypothesis testing, we will always set up a particular hypothesis that we want to demonstrate to be true. We then use probability to determine the likelihood of our hypothesis is correct. If it appears our original hypothesis was wrong, we reject it and accept the alternative hypothesis. The alternative hypothesis is usually the opposite of our original hypothesis. In Fisher’s case, his original hypothesis was that the lady was guessing. His alternative hypothesis was the lady was not guessing.
Generally speaking, the hypotheses that business researchers want to prove are stated in the alternative hypothesis.
Thus, the statement 'In testing hypotheses, the researcher initially assumes that the alternative hypothesis is true and uses the sample data to reject it' is False.
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Find the domain of F(x)=8/x
Answers
Since divisions by zero is ill-defined, the domain for F(x)=8/x includes any real integers other than x=0. F(xdomain )'s is therefore (-infinity, 0) U (0, +infinity).
The definition of domainDescribe domain. The term "domain," which is unique to the internet, can apply to both the structure of the internet and the organization of a company's network resources. A domain is typically a sphere of information or a governing region.
What characteristics define a domain?A function's domain is the set of all potential inputs. For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.
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Resolve the vector combinations below:
a. 45 m S and 35 m S
b. 15 m N and 60 m S
c. 5 m S, 10 m E, and 7m W
Answers
a. 45 m S and 35 m S: This vector combination resolves to 10 m S.
b. 15 m N and 60 m S: This vector combination resolves to 45 m S.
c. 5 m S, 10 m E, and 7m W: This vector combination resolves to 8 m E.
What is the vector?Vectors can be added, subtracted, and multiplied by scalars (numbers) to create new vectors. In physics, vectors are used to represent quantities such as velocity, force, and acceleration.
They can also be used in other fields such as engineering, computer graphics, and economics. Vectors can be represented in different ways, such as in Cartesian coordinates (x, y, z) or polar coordinates (magnitude, angle).
a. The vector combination of 45 m S and 35 m S is 10 m S. This is because the vectors are pointing in the same direction (south) and the magnitude of the resultant vector is the sum of the magnitudes of the individual vectors.
b. The vector combination of 15 m N and 60 m S is 45 m S. This is because the vectors are pointing in opposite directions (north and south) and the magnitude of the resultant vector is the difference of the magnitudes of the individual vectors.
c. The vector combination of 5 m S, 10 m E, and 7 m W is 8 m E. This is because the vectors are pointing in different directions (south, east, and west) and the magnitude of the resultant vector is found using the Pythagorean theorem.
The east and west vectors can be viewed as the legs of a right triangle, with the resultant vector being the hypotenuse. The magnitude of the resultant vector is the square root of the sum of the squares of the individual vectors.
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The graph below shows a linear relationship between x and y. Assume that both the x-axis and the y-axis have the same scale. Determine the value of the constant rate of change of y with respect to x (This is a numerical value.) Write a formula that expresses change in y in terms of change in x. Suppose that y = 1.5 when x=1 Write a formula that expresses y in terms of x.
Answers
The value of the constant rate of change of y with respect to x is 20.
A formula that expresses change in y in terms of change in x is y = kx.
Suppose that y = 1.5 when x = 1, a formula that expresses y in terms of x is k = 1.5.
How to determine the value of the constant rate of change?In Geometry, the rate of change of any straight line simply refers to its gradient or slope and it can be calculated by using this mathematical expression;
Rate of change (slope), m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)
Assuming that both the x-axis and the y-axis have a scale of 1:20, the constant rate of change is given by:
Constant rate of change = 20/1 = 20.
When y = 1.5 and x = 1, a formula that expresses y in terms of x is given by:
y = kx
k = y/x
k = 1.5/1
k = 1.5.
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Which table shows a proportional relationship between X and Y?
K12
Answers
X and Y don't have a proportionate relationship.No, not all yx ratios are equal.
What is a ratio?If the ratios of two or more numbers or variables are equal to one another, they are said to be in proportion.
The answer to the query is
8; 10, 12; 14, given x
y : 5, 7, 9, 11
Ratios between various x and y values are not comparable.
( 8 /5)
≠ (10 / 7)
≠ (12 /9)
≠(14 /11)
We get to the conclusion that x and y have no proportional relationship.
Hence, Option(1) is the correct answer.
X and Y don't have a proportionate relationship.No, not all yx ratios are equal.
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Use the properties of exponents to generate an expression equivalent to each expression.
[tex](x^3y^7)^2[/tex]
[tex](144^3)^\frac{1}{6}[/tex]
[tex]2^(3t+4)[/tex]
Answers
x⁶y¹⁴ is the expression equivalent to (x³y⁷)², 12 is the equivalent expression of [tex](144^{3}) ^{\frac{1}{6} }[/tex] and 6t+8 is equivalent expression of 2(3t+4).
What is Expression?An expression is combination of variables, numbers and operators.
Equivalent expressions are expressions that work the same even though they look different.
The given expression is (x³y⁷)²
(x³)²(y⁷)²
x⁶y¹⁴
x⁶y¹⁴ is the expression equivalent to (x³y⁷)²
Expression is [tex](144^{3}) ^{\frac{1}{6} }[/tex]
[tex]144^{\frac{3}{6} }[/tex]
[tex]144^{\frac{1}{2} }[/tex]
√144
12
12 is the equivalent expression of [tex](144^{3}) ^{\frac{1}{6} }[/tex]
Expression is 2(3t+4)
Apply distributive property
6t+8
6t+8 is equivalent expression of 2(3t+4).
Hence, x⁶y¹⁴ is the expression equivalent to (x³y⁷)², 12 is the equivalent expression of [tex](144^{3}) ^{\frac{1}{6} }[/tex] and 6t+8 is equivalent expression of 2(3t+4).
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What is the greatest number that evenly divides the sum of any three consecutive whole numbers
Answers
The greatest number that evenly divides the sum of any three consecutive whole numbers is three.
What is an Integer?
This is referred to as a whole number that can be positive, negative, or zero and we should note that it doesn't a fractional number and examples include 0, 2, -3 etc.
The product of any three consecutive integers is always divisible by 3 and the addition of any 3 consecutive numbers together it will always equal a multiple of 3 which is therefore the reason why it was chosen as the correct choice.
An example is n+2 is an integer, 3(n+2) is divisible by 3 in this scenario hence 3 is the correct choice.
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A couple ordered 50 ounces of pate for their engagement party of 36 people. The pate was such a hit that the couple has decided to serve it again at their wedding reception. How many ounces of pate should they order for 296 people?
Answers
The quantity of ounce of pate they should order for the 296 people which will be present for their wedding reception would be = 411.1 ounce.
How to calculate the quantity of ounce of pate?The quantity of ounce ordered for 36 people = 50 ounce.
Therefore the quantity of ounce that will be enough for 296 people = X ounce.
Make X ounce the subject of formula;
X ounce = 296 × 50 /36
= 14800/36
= 411.1 ounce.
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-11x-14x-26=-25-25x-1
What kind of equation is it
Answers
Answer:
Linear equation with one variable
Step-by-step explanation:
Here, that one variable is x.
- 11x - 14x - 26 = - 25 - 25x - 1
- 25x - 26 = - 25x - 25 - 1
- 25x - 26 = - 25x - 26
Multiply - 1 on both sides,
25x + 26 = 25x + 26
This equation has infinite solutions.
Where value you substitute in place of x, you will the same answer on the both the sides.
State if the two triangles are congruent. If they are, state how
you know.
Answers
Explanation:
ASA = angle side angle
The marked side is between the marked angles.
The markings on the angles tell us which angles pair up to be congruent. The tickmark on the sides tell us the sides are congruent.
AAS is similar to ASA, but with AAS the marked side isn't between the marked angles.
We cannot use SAS since we don't know anything about another pair of sides.
Find the sum of 9x^2+5x+8 and 9x-7
Answers
Answer:
[tex]9x^2+14x+1[/tex]
Step-by-step explanation:
Hey there!
In order to find the answer to this problem, we must first form an equation; then we can solve/simplify it further
Our Equation:
----------------------------------------------------------------------------------------------------------
[tex](9x^2+5x+8)+(9x-7)[/tex]
1. Distribute the positive sign: positive and positive make positive, positive and negative make negative, negative and negative make positive
[tex]9x^2+5x+8+9x-7[/tex]
2. Combine like terms in each parenthesis: This means combining the x values and the constants.
[tex]9x^2+14x+1[/tex]
----------------------------------------------------------------------------------------------------------
This means that when you add the two given values, the answer you get is: [tex]9x^2+14x+1[/tex]
Solve for the solution to a system of equations using the following matrices and Cramer’s rule. Show your work.
A= [2 1] X= [5 1] Y= [2 5]
[1 3] [5 3] [1 5]
Answers
Graph the line
y=-1/3x-6
Answers
Please see the image attached below to know a representation of linear function y = - (1 / 3) · x - 6 in Cartesian plane.
How to graph a linear function
Linear functions are polynomials of the form:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variabley - Dependent variableGraphically speaking, linear functions represents lines and lines can be generated from two points on Cartesian plane. The procedure is described below.
First, obtain two points from linear function:
x = 0
y = - (1 / 3) · 0 - 6
y = - 6
x = 1
y = - (1 / 3) · 1 - 6
y = - 1 / 3
Second, add the points on Cartesian plane.
Third, construct a line that passes through the two points added. Please see the image attached below.
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Help me ASAP math question.
Answers
The value of x is 900 and value of y is 300.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
From the given information we form a system of linear equations.
1.4x+1.6y=1740..(1)
x-3y=0..(2)
x=3y
Plug in x =3y in the equation 1.
1.4(3y)+1.6y=1740
4.2y+1.6y=1740
5.8y=1740
Divide both sides by 5.8
y=300
x=3(300)=900
Hence, the value of x is 900 and value of y is 300.
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Multiply Both Equations to Eliminate a Variable
5.x - 3y = 6
2x + 5y = -10
Answers
The value of x and y obtained when multiplying equations to eliminate variable is y = -62/40 and x = -18/16.
What is elimination method?The elimination approach involves taking one variable out of the system of linear equations by utilizing addition or subtraction together with multiplication or division of the variable coefficients.
The given equations are:
5x - 3y = 6, and
2x + 5y = -10
Isolate the value of x in the following equation:
5x - 3y = 6
5x = 6 + 3y
x = (6 + 3y)/5
Substitute the value of x as follows:
2x + 5y = -10
(2) (6 + 3y)/5 + 5y = -10
12 + 15y + 25y = -50
40y = -50 -12
40y = -62
y = -62/40
Substitute the value of y to find the value of x:
2x + 5(-62/40) = -10
16x - 62 = -80
16x = -80 + 62
16x = -18
x = -18/16
Hence, the value of x and y obtained when multiplying equations to eliminate variable is y = -62/40 and x = -18/16.
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i forget joint frequency
Answers
The joint frequency of adults who voted for chocolate is given as follows:
0.1148.
How to calculate a joint frequency?A relative frequency is calculated as the division of the number of desired outcomes by the number of total outcomes.
A joint frequency is calculated considering a combination of two events.
In the context of this problem, we have that out of 122 people, there are 14 adults who voted for chocolate, hence the joint frequency of adults who voted for chocolate is obtained as follows:
14/122 = 0.1148.
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Which of the following are square properties? Choose ALL that apply.
Diagonals are congruent.
Exactly one pair of parallel sides.
Four right angles.
Diagonals are perpendicular.
Answers
I hope this helps<3
question 1(multiple choice worth 1 points) (06.11 mc) identify the improper integral(s): the integral from 2 to 5 of dx over quantity x squared minus 1 the integral from 1 to infinity of quantity x minus 1 dx the integral from negative 2 to 3 of dx over quantity x plus 1 i and ii ii and iii i only iii only
Answers
The improper integrals are i and ii.
Improper integral
An improper integral is the limit of a definite integral in mathematical analysis when either one endpoint of the interval of integration approaches a limit, such as a real number, positive or negative infinity, or, in rare cases, when both endpoints approach limits.
According to the question
The first integral, the integral from 2 to 5 of dx over amount x squared minus 1, is incorrect because the denominator x2-1 becomes 0 at x=1, meaning the integrand expands to infinity at these places and the integral is not convergent across the range [2,5]. Since the interval of integration extends from 1 to infinity and the function is not limited, the second integral, the integral from 1 to infinity of amount x minus 1 dx, is incorrect. The integrals I and ii are both incorrect. The third integral, which is a standard integral and is the integral from negative 2 to 3 of dx over amount x + 1, is convergent.
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Oliver read for 450450450 minutes this month. His goal is to read for 10\%10%10, percent more minutes next month.
If Oliver meets his goal, how many minutes will he read in all during the two months?
Answers
Using percentages we know that he read for 945 minutes over two months, covering pages. If Oliver accomplishes his goal of reading for 19% more minutes next month.
What is the percentage?Since one percent (symbolized as 1%) is equal to one-hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.
So, this month, Oliver read for 450 minutes.
He has promised to read for 10% extra minutes the following month.
Next month, he spent minutes reading pages:
450 + 10% * 450 = 450 + 45 = 945
He, therefore, read for pages at a time for two months = 450+495=945
Hence He read for 945 minutes over two months, covering pages.
Therefore, using percentages we know that he read for 945 minutes over two months, covering pages. If Oliver accomplishes his goal of reading for 19% more minutes next month.
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A and B are the parallel. Find the missing angles.
125
55
35
Answers
Answer:
Step-by-step explanation:
Find the break-even point for the given cost and revenue equations. Round to the nearest whole unit.
C = 20n + 134,000
R = 160n
Answers
Answer:
in break-even point
C=R
20n+134000=160n
134000= 160n-20n
140n=134000
n=134000/140
n=957.14
n=957 ( nearest whole number)
C= 20(957.14) + 134000
= 153142.8
= 153143 (nearest whole number)
R= 160(957.14)
=153142.4
= 153142 (nearest whole number)
you are given a mc test where each question has four possible answers. the test is made up of 12 questions and you did not prepare for the test. the number of answers possible is
Answers
Since the MCQ test has twelve questions with each question having four possible answers, the number of ways in which the test can be answered are 16777216.
There are 12 questions in the given test. It has an MCQ test and every question in the test has 4 options, that is, 4 possible answers.
There are multiple possibilities by which the given test can be answered as we can select a different option every time while answer a question. To calculate the different amount of possibilities,
By the fundamental principle of counting,
The amount of possible ways to answer one question are
4¹ = 4
The amount of possible ways to answer 12 questions are
4¹² = 16777216
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Does the equation below define a linear function?
y = -x³ - 11
Explain how you got your answer.
Answers
The equation does not define a linear function
How to determine the type of the functionFrom the question, we have the following parameters that can be used in our computation:
y = -x³ - 11
As a general rule, a linear equation is any equation that has a degree of 1
The given equation above has a degree of 3
Hence, it is not a linear equation
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I know each x_i (i = 1, 2, ..., n) is a random variable based on the sample size n obtained. Therefore, [tex]\frac{}{X}[/tex] is a random variable since it would be a different (random) value for each new sample size of n collected. How would I further elaborate on this explanation to answer the question in the screenshot?
Answers
The sample mean can be classified as a random variable because it is calculated from the sample which is built as random.
How to obtain the mean of a data-set?The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.
Hence the sample mean is obtained as the sum of all observations of the sample divided by the sample size.
As the observations of the sample are taken at random, the sum of these observations will be a random variable, and so will the sample mean.
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NO LINKS!!!!
Please help me with #4
Answers
Answer:
C) To know whether 2 triangles are similar, it is enough to know the measure of 2 angles in each triangle.
Step-by-step explanation:
Two triangles are said to be similar if:
corresponding angles are the same size, andcorresponding sides are in the same ratio.As there are three interior angles in a triangle, and the sum of the interior angles is always 180°, we need to know the measure of at least 2 angles in each triangle to determine if they are similar. The known angles don't have to be corresponding angles, as we can calculate the third angle and then compare all three angles to determine if the triangles are similar.
With regards to the sides of a triangle, it is not enough to know the measure of 2 sides to determine if they are similar. We would need to know at least one interior angle in this case.
Sketch an angle θ in standard position such that θ has the least possible positive measure, and the point (0,-2) is on the terminal side of θ. Then find the values of the six trignometric functions for the angle. Rationalize deniminators is applicable. Do not use a calculator.
Find sin θ, cos θ, tan θ, csc θ, sec θ, and cot θ.
If it is undefined, say undefined.
Answers
The values of the six trignometric functions for the angle are
Sinθ = Sin(3π/2) = -1Cosθ = Cos(3π/2) = 0tanθ = tan(3π/2) = undefined Cotθ = Cot(3π/2) = 0Cscθ = Csc(3π/2) = 1Secθ = Sec(3π/2) = undefinedThe above sketch an angle θ in standard position such that θ has the least possible positive measure, and the point (0,-2) is on the terminal side of θ. We have to determine the value of six
triganomertric functions at angle θ. As we see at terminal side point (0,-2) the value of angle θ = 3π/2. The six trigonometric functions are sine, cosine , secant , cosecant , tangent , cotangent .
Now, Sinθ = Sin(3π/2) = Sin( π + π/2)= Sin ( 180° + π/2) = - sin(π/2) ( since, 180° + θ represents 3rd quadrant where sinθ is negative)
=> Sinθ = - 1
Cosθ = Cos(3π/2) = Cos( π + π/2)= Cos( 180° + π/2) = - Cos(π/2) ( since, 180° + θ represents 3rd quadrant where cosθ is negative)
=> Cosθ = Cos(π/2) = 0
tanθ = tan (3π/2) = tan( π + π/2)= tan( 180° + π/2) = - tan(π/2) ( since, 180° + θ represents 3rd quadrant where tanθ is positive)
=> tanθ = - sin(π/2)/cos(π/2) = 1/0
= undefined
Cscθ = Csc(3π/2) = Csc( π + π/2)= Csc( 180° + π/2) = - Csc(π/2) ( since, 180° + θ represents 3rd quadrant where cscθ is negative)
=> Cscθ = - Csc (π/2) = - 1/sin(π/2) = 1
Secθ = Sec(3π/2) = Se( π + π/2)= Sec( 180° + π/2) = - Sec(π/2) ( since, 180° + θ represents 3rd quadrant where secθ is negative)
=> Secθ = -Sec(π/2) = -1/cos(π/2) = - 1/0
= undefined
Cotθ = Cot(3π/2) = Cot( π + π/2)= Cot( 180° + π/2) = Cot(π/2) ( since, 180° + θ represents 3rd quadrant where cotθ is positive)
=> Cotθ = cot(π/2) = Cos(π/2)/sin(π/2) = 0
Hence, we determined all required triganomertric functions value for θ=3π/2.
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The six trignometric functions' values for the angle are
Tan = tan(3/2) = undefined, Sin = Sin(3/2) = -1, Cos = Cos(3/2) = 0, and vice versa.
Cot = Cot(3/2), Csc = Csc(3/2), and Sec = Sec(3/2), respectively.
The above drawing shows an angle in standard position with the point (0,-2) on the angle's terminal side and the smallest positive measure achievable. We must calculate the value of six.
Triganomertric operates at an angle. As can be seen, the angle's value is 3/2 at the terminal side point (0,-2). In trigonometry, there are six different functions: sine, cosine, secant, cosecant, tangent, and cotangent.
At this point, Sin = Sin(3/2) = Sin( + /2)
= Sin ( 180° + π/2) Since 180° + denotes the third quadrant, where sin is negative, the expression is equal to - sin(/2).
=> Sinθ = - 1
Cos is equal to Cos(3/2) = Cos(+/2)
because 180 degrees, = Cos(180° + /2) = - Cos(/2)
Since 180° + denotes the third quadrant, where cos is negative, the equation is Cos(180° + /2) = - Cos(/2).
Hence, Cos = Cos(/2) = 0.
Tan is equal to Tan (3/2) = Tan (+/2)
= tan( 180° + π/2) Since 180° + denotes the third quadrant, where tan is positive, the expression is = - tan(/2).
Consequently, tan = - sin(/2)/cos(/2) = 1/0
not defined
Csc is equal to Csc(3/2) = Csc(+/2)
Since 180° + represents the third quadrant, where csc is negative, Csc(180° + /2) = - Csc(/2)
=> 1/sin(/2) = 1 = Csc = - Csc (/2)
Se( + /2) = Se( = Sec(3/2)
Since 180° + represents the third quadrant, where sec is negative, sec(180° + /2) = - Sec(/2)
The formula is: Sec = -Sec(/2) = -1/cos(/2) = -1/0.
not defined
Cot = Cot(3/2), which equals Cot(+/2)
Since 180° + denotes the third quadrant, where cot is positive, the equation is Cot(180° + /2) = Cot(/2).
Consequently, Cot = Cot(2/2) = Cos(2/2)/sin(2/2) = 0
As a result, we calculated the values for all necessary triganomertric functions for 3/2.
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