Draw the angle 0=-pi/2 in standard position find the sin and cos

Answers

Answer 1

An angle in standard position has the vertex at the origin and the initial side is on the positive x-axis.

Thus, the initial side of the angle is:

Now, half the circumference measures pi, thus, pi/2 is a quarte of the circumference. As we want to find the angle -pi/2, then we need to rotate the terminal side clockwise:

Find the sine and the cosine.

The sine and the cosine in the unit circle are given by the coordinates as follows:

[tex](\cos\theta,\sin\theta)[/tex]

As can be seen in the given unit circle, the terminal side is located at:

[tex](0,-1)[/tex]

Thus, the values of cosine and sine are:

[tex]\begin{gathered} \cos\theta=0 \\ \sin\theta=-1 \end{gathered}[/tex]

Related Questions

Solve 3 (4x - 7) * 7x - 10 0 12x - 7 12x - 21 12x + 21

Answers

Answer:

12x-21

Explanation:

Given the expression

3 (4x-7)

On expanding using distributive law;

3(4x-7)

3(4x) - 3(7)

12x - 21

Hence the result required is 12x-21

What is the polar form of the equation? What type of polar curve is this?

Answers

The curve is given to be:

[tex]x^2+y^2+12y=0[/tex]

We can rewrite the equation in the form:

[tex]\frac{\left(x-h\right)^2}{a^2}+\frac{\left(y-k\right)^2}{b^2}=1[/tex]

Using the Completing the Square method, we have the equation to be:

[tex]\frac{\left(x-0\right)^2}{6^2}+\frac{\left(y-\left(-6\right)\right)^2}{6^2}=1[/tex]

Therefore, the ellipse's center is (0, -6).

Section 5.2-4 Graph the following system of equations and find the solution. Plot the solution on the graph. Enter your answer as (x,y). -2x-3y = 0 x+3y = 3 1 2 3 4 5 -1 -2 -3 -4 -5 1 2 3 4 5 -1 -2 -3 -4 -5 Clear All Draw: LineDot Solution =

Answers

For finding y, we can replace the value of x in any equations.

Solution (-3,2)

Plot graphs

I need help with geometry!

Answers

Basic geometry are formulars and properties of basic shapes like rectangle, square, circle, triangle, and solid shapes like cuboid, cube cylinder etc.

The area, perimeter and volume of solid shape are properties that can be determined from this shape.

Perimeter is the sum of the whole side of the figure. Example the perimeter of a rectangle with 2 length and 2 width can be calculated by adding the whole 2 length and width.

The perimeter of the rectangle above is by adding all the sides.

perimeter = 4 + 4 + 2 + 2 = 12 cm

The area of the figure below is the amount of space of the boundary. The area of the rectangle below is length * width = 4 * 2 = 8 cm squared.

Find the value of z that makes quadrilateral EFGH a parallelogram.2zz+10FEHGz=Submit

Answers

In a parallelogram opposite sides have the same length therefore, for figure EFGH to be a parallelogram we must have that:

[tex]GF=HE[/tex]

Substituting we get:

[tex]z+10=2z[/tex]

Now, we solve for "z". First, we subtract "z" from both sides:

[tex]\begin{gathered} z-z+10=2z-z \\ 10=z \end{gathered}[/tex]

Therefore, the value of "z" is 10.

Write this trinomial in factored form. 5a² - 30 - 14

Answers

[tex]5x^2-3x-14[/tex]

replace x with a for this exercise

we use this formula to factor

[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]

where a=5, b=-3 and c=-14

[tex]x=\frac{-(-3)\pm\sqrt[]{(-3)^2-4(5)(-14)}}{2(5)}[/tex][tex]\begin{gathered} x=\frac{3\pm\sqrt[]{9+280}}{10} \\ \\ x=\frac{3\pm\sqrt[]{289}}{10} \\ \\ x=\frac{3\pm17}{10} \end{gathered}[/tex]

we have two roots

[tex]\begin{gathered} x=\frac{3+17}{10} \\ x=2 \end{gathered}[/tex]

and

[tex]\begin{gathered} x=\frac{3-17}{10} \\ \\ x=-\frac{7}{5} \end{gathered}[/tex]

so the simplified equation is

[tex](x-2)(x+\frac{7}{5})[/tex]

now replace x for a

[tex](a-2)(a+\frac{7}{5})[/tex]

A woman who has recovered from a serious illness begins a diet regimen designed to get her back to a healthy weight. She currently weighs 106 pounds. She hopes each week to multiply her weight by 1.04 each week.

Answers

The required exponential function would be W = 106 × 1.04ⁿ for the weight after n weeks.

What is an exponential function?

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

It is a relation of the form y = aˣ in mathematics, where x is the independent variable

The given starting weight for the diet program is 106 pounds. Because the weight is expected to be multiplied by 1.04 pounds each week, the weight will develop exponentially with an initial value of 106 pounds and a growth factor of 1.04 pounds. Then, for the weight after weeks, the exponential function is given by,

W = W(n) = Pb'

Here P = 106 and b = 1.04

Hence the required formula is,

⇒ W = 106 × 1.04ⁿ

Thus, the required exponential function would be W = 106 × 1.04ⁿ for the weight after n weeks.

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The question seems to be incomplete the correct question would be

Choose the algebraic description that maps ΔABC onto ΔA′B′C′ in the given figure.Question 7 options:A) (x, y) → (x + 4, y + 8)B) (x, y) → (x + 8, y + 4)C) (x, y) → (x – 4, y – 8)D) (x, y) → (x + – 8, y – 4)

Answers

Step 1

Given the triangle, ABC translated to A'B'C'

Required to find the algebraic description that maps triangle ABC and A'B'C'

Step 2

The coordinates of points A, B,C are in the form ( x,y)

Hence

[tex]\begin{gathered} A\text{ has a coordinate of ( -3,-2)} \\ B\text{ has a coordinate of (-6,-5)} \\ C\text{ has a coordinate of (-1,-4)} \end{gathered}[/tex]

Step 3

Find the algebraic description that maps triangle ABS TO A'B'C'

[tex]\begin{gathered} A^{\prime}\text{ has a coordinate of (5,2)} \\ B^{\prime}\text{ has a coordinate of ( 2,-1)} \\ C^{\prime}\text{ has a coordinate of ( 7, 0)} \end{gathered}[/tex]

The algebraic description is found using the following;

[tex]\begin{gathered} (A^{\prime}-A^{})=(x^{\prime}-x,\text{ y'-y)} \\ OR \\ (B^{\prime}-B)=(x^{\prime}-x,\text{ y'-y)} \\ OR \\ (C^{\prime}-C)=(x^{\prime}-x,\text{ y'-y)} \end{gathered}[/tex]

Hence,

[tex]\begin{gathered} =\text{ ( 5-(-3)), (2-(-2))} \\ =(8,4) \\ \text{Hence the algebraic description from triangle ABC to A'B'C' will be } \\ =(x,y)\Rightarrow(x\text{ + 8, y+4)} \end{gathered}[/tex]

Hence the answer is option B

Patrick is buying a new car. He can choose the body style, color and engine type. If there are 54 ways he can select a car, with there body styles and two engine choices , his many colors are available

Answers

Given:

Total Number of ways = 54

Number of body styles = 3

Number of engine choices = 2

Let's find the number of colors available.

To find the number of colors available, we have:

Number of ways = Number of body styles x Number of engine choices x Number of colors

54 = 3 x 2 x c

Where c represent the available number of colors.

Let's find c.

54 = 3 x 2 x c

54 = 6c

Divide both sides by 6:

[tex]\begin{gathered} \frac{54}{6}=\frac{6c}{6} \\ \\ 9=c \\ \\ c=9 \end{gathered}[/tex]

Therefore, there are 9 colors available to select from.

ANSWER:

a person who weighs 145 pounds on Earth would weigh 47.2 pounds on Mercury. How much would a person weigh on Mercury if they weigh 135 pounds on Earth?

Answers

A person weigh on the Mercury if they weigh 135 pounds on Earth is 43.94 pounds.

Weight of person on Earth = 145pounds

145 = mg

Weight of person on Mercury = 47.2pounds

47.2 = ma

145/47.2 = mg/ma

145/47.2 = g/a

a = 47.2g/145 .....1.

If weight of person on earth = 135pounds

135 = mg

m = 135/g .......2.

Then, Weight of person on Mercury = ma

using the above values of a and m we we get

= (135/g)x (47.2g/145 )

= 135 x 47.2 / 145

= 43.94 pounds

A person weigh on the Mercury if they weigh 135 pounds on Earth is 43.94 pounds.

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Which expression is equivalent to (m−5n−3)−3?

m−15n−9
m15n9
m−8n−6
1 over the quantity m raised to the eighth power times n raised to the sixth power end quantity

Answers

The expression (m⁻⁵n⁻³)⁻³ has an equivaent of m⁻¹⁵n⁹

How to determine the equivalent expression

From the question, the expression is represented as

(m−5n−3)−3

Rewrite the expression properly

This is done as follows;

(m⁻⁵n⁻³)⁻³

Open the brackets

So, we have the following equation

(m⁻⁵n⁻³)⁻³ = (m⁻⁵)⁻³ x (n⁻³)⁻³

Evaluate the products

So, we have the following equation

(m⁻⁵n⁻³)⁻³ = (m⁻¹⁵) x n⁹

This gives

So, we have the following equation

(m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹

Hence, the solution is (m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹

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The given expression (m⁻⁵n⁻³)⁻³ has an equivalent to the m⁻¹⁵n⁹

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The expression is represented as (m−5n−3)−3

Rewrite the expression as follows;

(m⁻⁵n⁻³)⁻³

Open the brackets , we have

(m⁻⁵n⁻³)⁻³ = (m⁻⁵)⁻³ x (n⁻³)⁻³

Evaluate the products, we have;

(m⁻⁵n⁻³)⁻³ = (m⁻¹⁵) x n⁹

(m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹

Hence, the solution will be; (m⁻⁵n⁻³)⁻³ = m⁻¹⁵n⁹

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I need a little understanding on a one page math assignment

Answers

[tex]\begin{gathered} The\text{ charge of 1 cubic yards at EZ excavation is}\Rightarrow\frac{196}{8}=24.5\text{ \$} \\ The\text{ charge of 1 cubic yards at Happy service is}\Rightarrow25\text{ \$} \\ (a)\text{ For 40 cubic yards is,} \\ At\text{ EZ excavation}\Rightarrow40\times24.5=\text{ \$980} \\ At\text{ Happy service}\Rightarrow40\times25=\text{ \$1000} \end{gathered}[/tex]

Write the expression as a complex number in standard form.
(-2+6i)-(2-3i)=

Answers

Answer:

-4 +9i

Step-by-step explanation:

complex number in standard form.

(-2+6i)-(2-3i)=

Combine like terms

-2 -2 +6i +3i

Standard form is a+bi

-4 +9i

How many -digit even numbers are possible the digit cannot be zero?

Answers

is –6, –4, –2, 0, 2, 4, 6

Answer:

45,000

Step-by-step explanation:

Hey! Let's help you with your question here!

So, let's think about this logically. The only limit we have here is that the leftmost digit cannot be zero. This makes sense because there would be no five-digit number if the leftmost is zero. In order to find the possible amount of even numbers, we need to take the possible numbers of each digit and have them multiplied to each other to get the total. (I will explain this soon).

First Digit:

Since, the rules state that the leftmost digit cannot be zero, this would be the digit that the rule affects. From here, we can have a possibility of the numbers 1 through 9 here. So, for the first digit, we have the possibility of 9 numbers that can be here.

Second, Third, Fourth Digit:

Now you're probably wondering as to why I've grouped up these 3 digits and not the last or the first one. We'll get to the last one in the next explanation, but we exclude the first digit because the rule that affects the first digit, does not affect these digits nor the last digit. With these 3 digits, we don't have that rule of it cannot be zero, so now our possibilities for what the numbers can be is 0 through 9. If we include 0 as a number too, then we have a possibility of 10 numbers that can be within these digits.

Fifth (Last) Digit:

For this last digit, there is an implicit rule being stated for the last digit. The question asks how many five-digit even numbers are possible if the leftmost digit cannot be zero. This rule affects the last digit only as that allows the whole five-digit number to be even and zero is included in this. So, the even numbers are 0, 2, 4, 6, and 8. In this case, we only have 5 possible numbers to choose from for the very last digit.

Answer Explanation:

Before I begin answering, back in the very first paragraph, I said we need to take the possible numbers of each digit and multiply them altogether to get the total amount of possible values. Why do we do this? This is the idea of possibility combination. We multiply because we are taking in account all of the possible values whereas if we just add, we're only taking in account the maximum possible value of each possibility. So, let's calculate the answer now! For the first digit, we have a possibility of 9 numbers being there (1-9). For the Second, Third, and Fourth digit, we have a possibility of 10 numbers being there (0-9). And finally for the last digit, we have a possibility of only 5 numbers (0, 2, 4, 6, and 8). So, the total possible combination is:

[tex]9*10*10*10*5[/tex]

[tex]=45,000[/tex]

Therefore, we get 45,000 total possible five-digit even numbers where the leftmost digit cannot be zero.

What is the measure of ZTVU shown in the diagram below?VSV12°R120°TO A. 132O B. 66 °C. 54D. 108

Answers

The external angle formed by the secants equals one-half the difference of the intercepeted arcs. Therefore:

If I take a 45 min. break at 2:15pm what time do I come back?

Answers

The break time is 2:15 pm.

The time interval for break is 45 min.

Determine the time at which interval ends.

[tex]\begin{gathered} 2\colon15+00.45=2\colon60 \\ =3\colon00 \end{gathered}[/tex]

So break ends (individual come back) at 3:00.

What’s the correct answer answer asap for brainlist

Answers

The sentence in B uses the underlined word incorrectly. The kirt was clever in concocting a story about hossatye zot in trouble.

What is adjective ?An adjective is a word that generally modifies or describes a noun or noun phrase. Its semantic role is to alter the information provided by the noun.

Here the word,

Ingenious means smart and clever, whereas ingenuous means innocent and naïve. The clever villain in your favorite comic book series may devise devious plots, while the clever heroine is completely unaware.Despite the fact that the adjective ingenious is more closely related to the noun engine than to the word genius, a genius is more likely to have ingenious ideas. Ingenious invention of a self-cleaning house. So is calculating the math required to launch a rocket to the moon.

So here option B is vocabulary incorrect .

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Kareem ordered some books online and spent a total of . Each book cost and he paid a total of for shipping. How many books did he buy?
(a) Write an equation that could be used to answer the question above. First, choose the appropriate form. Then, fill in the blanks with the numbers , , and . Let represent the number of books.

(b) Solve the equation in part (a) to find the number of books.

Answers

Answer:

Step-by-step explanation:

y varies directly as x, y = 7 when x = 21. Determine x when y = 5.

Answers

y varies directly as x, y = 7 when x = 21. Determine x when y = 5.

Step 1

Let

y varies directly as x, it is y depends on x, in math terms

f(x)=y

y = 7 when x = 21

f(21)=7

Determine x when y = 5. f(?)=5

Step 2

there is a proportion, this must be equal, make a rule of three to find the value

x y

[tex]\begin{gathered} 21\leftrightarrow7 \\ x\text{ }\leftrightarrow5 \\ \text{the relation is} \\ \frac{21}{7}=\frac{x}{5} \\ \text{solve for x} \\ x=\frac{21\cdot5}{7} \\ x=\frac{105}{7} \\ x=15 \end{gathered}[/tex]

so , when y=5, x=15

In the figure below, m2 = 49. Find mx 1.

Answers

By definition, a Right angle is an angle that measures 90 degrees.

Complementary angles are those angles that add up to 90 degrees.

For this case, you can identify that the angle 1 and the angle 2 are Complementary angles, because when you add them, you get 90 degrees (a Right angle).

Knowing the above, you can set up the following equation:

[tex]m\angle1+m\angle2=90\degree[/tex]

Since you know that:

[tex]m\angle2=49\degree[/tex]

You can substitute this value into the equation and the solve for the angle 1 in order to find its measure. You get that this is:

[tex]\begin{gathered} m\angle1+49\degree=90\degree \\ m\angle1=90\degree-49\degree \\ m\angle1=41\degree \end{gathered}[/tex]

The answer is:

[tex]m\angle1=41\degree[/tex]

what is 3 in the 9th power equal

Answers

3 in the 9th power means that you have to make 3 to the power of 9.

[tex]3^9=3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3=19,683[/tex]

The answer is 19,683.

what is the line that passes through points(-6,-10)(-2,-10)

Answers

The line passes through the points, (-6,-10) and (-2,-10)

We know equation of the line passing through points (x',y') and (x'',y'') is given by:

[tex]y-y^{\prime}=\frac{y^{\prime}^{\prime^{}}-y^{\prime}}{x^{\prime}^{\prime}-x^{\prime}}(x-x^{\prime})[/tex]

So the equation of the line is:

[tex]\begin{gathered} y-(-10)=\frac{-10-(-10)}{-2-(-6)_{}}(x-(-6)) \\ \Rightarrow y+10=0 \\ \Rightarrow y=-10 \end{gathered}[/tex]

The equation of the line is y=-10

What is the area of this triangle?
Pls help :(

Answers

24
Remember the formula
A=1/2(B)(H)

If y varies directly as x, and y is 6 when x is 72, what is the value of y when x is 8?
1/9
2/3
54
96

Answers

Answer:

2/3

Step-by-step explanation:

y = xk

6 = 72K Solve for k Divide both sides by 72

[tex]\frac{1}{12}[/tex] = k

y = xk

y = [tex]\frac{8}{1}[/tex] x [tex]\frac{1}{12}[/tex]

y = [tex]\frac{8}{12}[/tex] I can simplify by dividing the numerator and denominator by 4

y = 2/3

help meeeeeeeeee pleaseee !!!!!

Answers

For the given functions, we can write the sum as:

(f + g)(x) = 9x + 1

How to find the sum between functions?

Here we want to find the sum between functions f(x) and g(x), and in this case, we have:

f(x)= x - 8

g(x) = 8x + 9

The sum can be written as:

(f + g)(x) = f(x) + g(x)

Replacing the functions there we get:

(f + g)(x) = f(x) + g(x)

(f + g)(x) = (x - 8) + (8x + 9)

(f + g)(x) = x + 8x - 8 + 9

(f + g)(x) = 9x + 1

That is the sum of the functions.

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The function y=f(x) is graphed below. Plot a line segment connecting the points on ff where x=-1 and x=0. Use the line segment to determine the average rate of change of the function f(x) on the interval −1≤x≤0

Answers

Answer:

Aveage Rate of cCanege = 40

Explanation:

The line segment is drawn in the function below:

Using the line segment:

[tex]\begin{gathered} \Delta x=0-(-1)=1 \\ \Delta y=40-0=40 \end{gathered}[/tex]

Therefore, the average rate of change will be:

[tex]\text{ Average Rate of Change}=\frac{\Delta y}{\Delta x}=\frac{40}{1}=40[/tex]

The average rate of change is 40.

23.What is the missing piece of information required to provethese triangles congruent?a) QYQYb) NYPYC) ZN 2 Pd) QY is the perpendicular bisector

Answers

In this case, the information that is explicitly seen in the graph is that we have 2 pairs of equal sides.

The missing information, that can also be seen in the picture, is that we have a shared side that is QY.

If we applied the reflexive property, we know that:

[tex]QY\cong QY[/tex]

and then we know that we have 3 pairs of equal sides, what proves that the triangles are congruent.

Answer: QY = QY (Option A).

The average score for games played in the NFL is 22 and the standard deviation is 9.3 points. 41 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution.

a. What is the distribution of ¯x x¯
? ¯xx¯ ~ N( , )
b. What is the distribution of ∑x ? ∑x ~ N ( , )
c. P( ¯x > 19.8214) =
d. Find the 60th percentile for the mean score for this sample size.
e. P(20.6214 < x¯< 23.2262) =
f. Q1 for the x¯distribution =
g. P( ∑x > 829.0774) =

For part c) and e), Is the assumption of normal necessary? NoYes

Answers

Using the normal distribution and the central limit theorem, it is found that:

a) The distribution is: x¯ ~ N(22, 1.45).

b) The distribution is: ∑x ~ N(902, 59.55).

c) P( ¯x > 19.8214) = 0.9332 = 93.32%.

d) The 60th percentile for the mean score for this sample size is of 22.37 points a game.

e) P(20.6214 < x¯< 23.2262) = 0.6312 = 63.12%.

f) Q1 for the x¯distribution = 21 points a game.

g) P( ∑x > 829.0774) = 0.8888 = 88.88%.

Assumption of normality is not necessary, as the sample sizes are greater than 30.

Normal Probability Distribution

The z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].Also by the Central Limit Theorem, for the sum of n instances of a variable, the mean is of [tex]\n\mu[/tex] and the standard deviation is of [tex]\sigma\sqrt{n}[/tex].Finally, by the Central Limit Theorem, assumption of normality is only necessary when the sample size is less than 30.

For a single game, the mean and the standard deviation of the number of points scored are given as follows:

[tex]\mu = 22, \sigma = 9.3[/tex]

For the average of 41 games, the standard error is:

[tex]s = \frac{9.3}{\sqrt{41}} = 1.45[/tex]

Hence the distribution is: x¯ ~ N(22, 1.45).

For the sum of the 41 games, the mean and the standard error are given as follows:

41 x 22 = 902.[tex]s = 9.3\sqrt{41} = 59.55[/tex].

Hence the distribution is: ∑x ~ N(902, 59.55).

In item c, the probability is one subtracted by the p-value of Z when X = 19.8214, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem: