find the values of the six trigonometric functions for angle theta in standard position if a point with the coordinates (1, -8) lies on its terminal side
Answer:
cosФ = [tex]\frac{1}{\sqrt{65}}[/tex] , sinФ = [tex]-\frac{8}{\sqrt{65}}[/tex] , tanФ = -8, secФ = [tex]\sqrt{65}[/tex] , cscФ = [tex]-\frac{\sqrt{65}}{8}[/tex] , cotФ = [tex]-\frac{1}{8}[/tex]
Step-by-step explanation:
If a point (x, y) lies on the terminal side of angle Ф in standard position, then the six trigonometry functions are:
cosФ = [tex]\frac{x}{r}[/tex]sinФ = [tex]\frac{y}{r}[/tex]tanФ = [tex]\frac{y}{x}[/tex]secФ = [tex]\frac{r}{x}[/tex]cscФ = [tex]\frac{r}{y}[/tex]cotФ = [tex]\frac{x}{y}[/tex]Where r = [tex]\sqrt{x^{2}+y^{2} }[/tex] (the length of the terminal side from the origin to point (x, y)You should find the quadrant of (x, y) to adjust the sign of each function∵ Point (1, -8) lies on the terminal side of angle Ф in standard position
∵ x is positive and y is negative
→ That means the point lies on the 4th quadrant
∴ Angle Ф is on the 4th quadrant
∵ In the 4th quadrant cosФ and secФ only have positive values
∴ sinФ, secФ, tanФ, and cotФ have negative values
→ let us find r
∵ r = [tex]\sqrt{x^{2}+y^{2} }[/tex]
∵ x = 1 and y = -8
∴ r = [tex]\sqrt{x} \sqrt{(1)^{2}+(-8)^{2}}=\sqrt{1+64}=\sqrt{65}[/tex]
→ Use the rules above to find the six trigonometric functions of Ф
∵ cosФ = [tex]\frac{x}{r}[/tex]
∴ cosФ = [tex]\frac{1}{\sqrt{65}}[/tex]
∵ sinФ = [tex]\frac{y}{r}[/tex]
∴ sinФ = [tex]-\frac{8}{\sqrt{65}}[/tex]
∵ tanФ = [tex]\frac{y}{x}[/tex]
∴ tanФ = [tex]-\frac{8}{1}[/tex] = -8
∵ secФ = [tex]\frac{r}{x}[/tex]
∴ secФ = [tex]\frac{\sqrt{65}}{1}[/tex] = [tex]\sqrt{65}[/tex]
∵ cscФ = [tex]\frac{r}{y}[/tex]
∴ cscФ = [tex]-\frac{\sqrt{65}}{8}[/tex]
∵ cotФ = [tex]\frac{x}{y}[/tex]
∴ cotФ = [tex]-\frac{1}{8}[/tex]
A jewelry store is having a 45% off sale for all necklaces. During this sale, what is the cost of a necklace that regularly costs $59.98?
Answer:
32.99
Step-by-step explanation:
59.98(45%)=26.99
59.98-26.99=32.99
Answer:
$32.99, the discount took off $26.99.
Step-by-step explanation:
Good luck!
10a^2b^0 for a=–3, b=–8
Answer:
90Step-by-step explanation:
Substitute a = -3 and b = -8 to the expression 10a²b⁰:
10(-3)²(-8)⁰ = 10(9)(1) = 90
a⁰ = 1 for any real number
Answer:
90
Step-by-step explanation:
10a^2b^0
Let a=–3, b=–8
10 (-3)^2 ( -8)^0
10 * 9 *1
90
Solve:
a.) 5(x - 2) > -15
AND
b.) x/1 - 9 < -10
Answer:
a.) x>-1
b.) x/1 - 9 < -10
Step-by-step explanation:
a.)
5(x - 2) > -15
(divide both sides)
x-2>-3
(move the constant to the right)
x>-3+2
(calculate)
x>-1
(answer)
b.)
x/1 - 9 < -10
(divide)
x-9<-10
(move the constant to the right)
x<-10+9
(calculate)
x/1 - 9 < -10
(answer)
Jackson has 429 matchbox cars in his collection. If 4 out of 9 are blue cards, how many are not blue
An item has a listed price of $80. If the sales tax rate is 8%, how much is the sales tax (in dollars)?
Answer:
$6.40
Step-by-step explanation:
u have to multiply 80 by 0.08 (tax percent in decimal form)
Answer:
$6.4
Step-by-step explanation:
all you have to do is find 8% of 80 by doing 8x8, which equals 64, then dividing by 10. That gives you 6.4. Then check it on a calculator to make sure you did it correctly
The constant of proportionality of this table is
Cups of
blue paint
cups of
yellow paint
2 10
1
Answer:
Step-by-step explanation:
1/2
A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides.
Suppose the paper is 7"-wide by 9"-long.
a. Estimate the maximum volume for this box?
b. What cutout length produces the maximum volume?
Answer:
B
Step-by-step explanation:
To answer this question it is necessary to find the volume of the box as a function of "x", and apply the concepts of a maximum of a function.
The solution is:
a) V (max) = 36.6 in³
b) x = 1.3 in
The volume of a cube is:
V(c) = w×L×h ( in³)
In this case, cutting the length "x" from each side, means:
wide of the box ( w - 2×x ) equal to ( 7 - 2×x )
Length of the box ( L - 2×x ) equal to ( 9 - 2×x )
The height is x
Then the volume of the box, as a function of x is:
V(x) = ( 7 - 2×x ) × ( 9 -2×x ) × x
V(x) = ( 63 - 14×x - 18×x + 4×x²)×x
V(x) = 4×x³ - 32×x² + 63×x
Tacking derivatives, on both sides of the equation
V´(x) = 12×x² - 64 ×x + 63
If V´(x) = 0 then 12×x² - 64 ×x + 63 = 0
This expression is a second-degree equation, solving for x
x₁,₂ = [ 64 ± √ (64)² - 4×12*63
x₁ = ( 64 + 32.74 )/ 24
x₁ = 4.03 this value will bring us an unfeasible solution, since it is not possible to cut 2×4 in from a piece of paper of 7 in ( therefore we dismiss that value)
x₂ = ( 64 - 32.74)/24
x₂ = 1.30 in
The maximum volume of the box is:
V(max) = ( 7 - 2.60) × ( 9 - 2.60)×1.3
V(max) = 4.4 × 6.4 × 1.3
V(max) = 36.60 in³
To chek for maximum value of V when x = 1.3
we find the second derivative of V V´´, and substitute the value of x = 1.3, if the relation is smaller than 0, we have a maximum value of V
V´´(x) = 24×x - 64 for x = 1.3
V´´(x) = 24× 1.3 - 64 ⇒ V´´(x) < 0
Then the value x = 1.3 will bring maximum value for V
Related Link: https://brainly.com/question/13581879
Write an inequality representing the following phrase:
One-tenth of a number h is less than or equal to ten
Answer:
[tex]\frac{1}{10} h\leq 10[/tex]
Step-by-step explanation:
Basically, we are just translating the phrase into an algebraic expression.
a diver descended 84 feet in 6 minutes. What was the divers change in depth per minute? Write and expression with a solution
Answer:
14 depth per minute
Step-by-step explanation:
84/6 = 14
Ms Liu has $40 to buy water and popcorn at the movie theater. Popcorn costs $8 per bag and water costs 3$ per bottle. write an algebraic expression that will be used to find the amount of money left when Ms. Liu 3 bags of popcorn and 4 bottles of water.
Answer:
S = 1 bag of popcorn
Y = 1 water
Step-by-step explanation:
S x 3 + Y x 4 = R
40 - R = (The Answer)
I need help. Is this right????
Answer: (I can only see stage 1 and 2 fully) Stage 1: 2 Stage 2: 4
Step-by-step explanation:
Answer:
Step-by-step explanation:
0 = 0
1 = 2
2 = 4
3 = 6
20 = 40
Consider the experiment of selecting a playing card from a deck of 52 playing cards. Each card corresponds to a sample point with a 1 52 probability.
Required:
a. List the sample points in the event a jack is selected.
b. List the sample points in the event a club is selected.
c. List the sample points in the event a face card ( jack, queen, or king) is selected.
d. Find the probabilities associated with each of the events in parts (a), (b), and (c).
Answer:
Kindly check explanation
Step-by-step explanation:
A deck of card:
Number of hearts = 13
Diamond = 13
Spade = 13
Club = 13
Each of heart, club diamond and spade has is numbered from (2,3,4,5,6,7,8,9,10,Ace, queen, Jack, king)
Hence, a club, diamond, spade and heart has one of each of the above numbers.
a. List the sample points in the event a jack is selected.
Jack : ( heart, club, diamond, spade)
B.) club is selected :
Cub : (Ace, 2, 3,4,5,6,7,8,9,10,king,queen,jack)
C)
Jack : ( heart, club, diamond, spade)
Queen : (heart, club, diamond, spade)
King : (heart, club, diamond, spade)
D) probability = required outcome / Total possible outcomes
P(jack selected) = 4 /52 = 1/13
P(club selected). = 13/52 = 1/4
P(face card selected) = 12 / 52 = 3/13
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Answer:
Y= -6x + 1
Step-by-step explanation:
Y=mx + b
M is your slope
B is your y intercept
The giber family purchased a house for 127,000 the first five years they paid off 12,000 each year . How much money do they still owe on the house ?
Answer:
dndnfhhfbdhdndndnmdmdndndnen
A map has a scale of 2 in: 6 mi. If Clayton
and Centerville are 10 in apart on the map
then how far apart are the real cities?
what is 4/6+2/3.?(these are fractions, you're just adding fractions)
Answer:
4/3
Step-by-step explanation:
Multiply 2 by 2, and get 4, then we multiply 3 by 2 and get 6.
Since our denominators match, we can add the numerators. 4 + 4 = 8. That gives us the sum, which is 8/6. Then you divide by 2. So 8/6 / 2 gives you 4/3.
Answer:
4/3 or 1 1/3
Step-by-step explanation:
1. 4/6 + 2/3
2. 4/6 + 4/6 You have to find the LCM (least common multiple) of the two denominators. In this case it would be 6. You have to multiply 3 by 2 to get 6. What you do to the bottom you also do to the top so you have to also multiply the numerator (2) by 2.
3. 4/3 or 1 1/3 Afterward, you just have to add straight across without changing the denominator and then if you need to simplify you simplify. Without simplifying, you would get 8/6, but, most teachers will mark it as wrong if you don't simplify. You can then change the improper fraction into a mixed number depending on what your teacher wants.
12 =7 solve.
Bro wat does this mean i dont get it please help someone :\
Answer:
if it says 12x = 7
the u will divide the 12 on both sides and x will equal to 7/12,,
if it simply says 12 = 7 then put false cause that's not true!!
What is the measure of angle F?
E. 20
D. 90
F.?
Answer:
the answer would be 70 because you take 90-20 and you get 70. you have a 90 degree angle is what you're working on right now
Step-by-step explanation:
BRAINLIEST Multiply each side by the common denominator
Answer:
c. x² + 2x -5 = 0
Step-by-step explanation:
Given expression;
[tex]\frac{5}{x}[/tex] = [tex]\frac{x + 2}{3}[/tex]
Unknown:
The quadratic equation equivalent to this expression:
Solution:
The common denominator here is 3x;
So, multiply both sides by 3x
[tex]\frac{5}{x}[/tex] x 3x = [tex]\frac{x + 2}{3} x[/tex] 3x
5 x 3 = (x + 2)x
15 = x² + 2x
So;
x² + 2x - 15
The quadratic expression is x² + 2x - 15
which number is the same as 0.000 000 1: 10^7 or 10^-7
Answer:
= 1 × 10^-7
(scientific notation)
= 1e-7
(scientific e notation)
= 100 × 10^-9
(engineering notation)
(billionth; prefix nano- (n))
= 0.0000001
(real number)
Step-by-step explanation:
10^7 = 10000000
What is the area of a rectangle with sides measuring 2x+3 and 3x-1 feet
1/5t+2- =17
1/5t
.1/5t
T=
Answer:
poop i forgot my ramen noodles are in the microwave
Step-by-step explanation:
What is the distance between the points (7, 8) and (-8, 0) on a coordinate grid?
1. You are eating on a Tootsie Roll Lollipop that is in the shape of a sphere. It is giving up volume at a steady rate of 0.25 in3 /min. How fast will the radius be decreasing when the Tootsie Roll Pop is .75 inches across?
Answer:
Step-by-step explanation:
Since the Tootsie Roll lollipop is a sphere
volume of sphere= [tex]\frac{4}{3}piR^3[/tex] = -0.25 [tex]in^3/min[/tex]
the negative sign indicates that the volume is decreasing
upon differentiating
as the diameter given is =0.75 so radius will be = 0.375
[tex]dV/dt = 4piR^2*dR/dt[/tex]
so [tex]dR/dt = 0.25/4*3.14 *(0.375)^2[/tex]
So the radius is decreasing at the rate of dR/dt= 0.142in/min
Find the product of (18k+ 2m)(m + k)
Answer:
18k^2+2m^2+20km
Step-by-step explanation:
A car sharing service offers a membership plan with a $50 per month fee that includes 10 hours of driving each month and charges $9 for each additional hour
(A) Write a piecewise definition of the cost F(x) for a month in which a member uses a car for x hours
(B) Graph F(x) for 0 < x s 15
(C) Find lim x--->10 F(x), lim x--->10F(x), and lim x--->10F(x), which- ever exist.
Answer:
A) F(x) = 50 + ( x - 10 )*9
B) Graph
C) lim ( x ⇒ 10) F(x) = 50
Step-by-step explanation:
A) F(x) = 50 + ( x - 10 )*9 since the first 10 hours are included in initial fee
B) In Annex
C) lim (x ⇒ 10) F(x) = 50 + ( 10 -10)*9
lim ( x ⇒ 10) F(x) = 50 + 0
lim ( x ⇒ 10) F(x) = 50
Name all rays with endpoint E
Answer: Is there an image??
AE, BE, CE, and DE is the rays with endpoint E.
What is a vector?An item with both magnitude and direction is referred to be a vector.
A vector can be visualized geometrically as a straight spline, with a pointing in the orientation and a length equal to the value of the vector.
Geometrical objects with magnitude and direction are called vectors.
A line with an arrow in its direction can also be used to represent a vector, and the length of the line relates to the vector's amplitude.
Given the figure,
The endpoint of all rays is E.
The rays associated with point E are;
AE, BE, CE, and DE
Hence "AE, BE, CE, and DE is the rays with endpoint E".
For more information about vector,
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Please help!!!- Find the measure of the angle in bold.
Need help to figure out to solve this.
Answer:
11x-6+(19x+6)=180°
11x+19x-6+6=180°
30x=180
x=180/30
x=6
it means that
19x+6=19*6+6=114+6=120°
Find the selling price of each item original plate price of gold fish at $7.65 discount 10%
Answer:
6.88 is what I think you're looking for
Step-by-step explanation: