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

Answers

Answer 1

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]    


Related Questions

What are the scale factor of ABC dilated to XYZ plz help

Answers

Answer:  B) 2/3

====================================

Explanation:

The order is important for ABC and XYZ so we can see what letters pair up.

A pairs with X since they are the first lettersB pairs with Y since they are the second lettersC pairs with Z since they are the third letters

Based on that, we can see that AB pairs with XY as they are the first two letters of ABC and XYZ respectively.

Divide the length XY over AB and reduce

XY/AB = 10/15 = 2/3

We could also divide XZ over AC

XZ/AC = 14/21 = 2/3

and we get the same ratio

Two sides of a triangle are equal in length. The length of the third side exceeds the length of one of the other sides by 3 centimetres. The perimeter of the triangle is 93 centimetres. Find the length of each side of the triangle

Answers

Answer:

it must be 30, 30, 33

Step-by-step explanation:

first, divide 93 by 3, since a triangle has 3 sides, you would get 31, yet if you took away that three in 93, it'd be 30. For that one that exceeds the others by 3, add the three to one of the thirds, and the other two are just the same, so when it said, "exceeds the length of one of the other sides," It didn't really change anything, because the other side is just as long.

What is the measure of ZRIA?
R
PA
N
999
.
A. 55
B. 30°
O C. 95°
D. 60°

Answers

The answer would be A

The measure of angle RIA is 55 degrees, option A is correct.

What is Coordinate Geometry?

A coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates.

We have to find the measure of angle RIA

The opposite angle of RIA is LIK

Let us find the measure of LIK

∠FIL+∠LIK+∠KIN=180

30+∠LIK+95=180

∠LIK + 125 =180

Subtract 125 from both sides

∠LIK = 180 - 125

=55 degrees

∠LIK is equal to ∠RIA

∠RIA = 55 degrees

Hence, the measure of angle RIA is 55 degrees, option A is correct.

To learn more on Coordinate Geometry click:

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4.8(x-1.75)= -9.6 but without the distributive property​

Answers

4.8(x-1.75)= -9.6
Answer:
x=0.55
X=.55
some teachers require you to put 0.55

-
y=2/3x + 2 and passes through the point (12, 6).
Find an equation perpendicular to the line
A. y=-3/2x + 21
B. y=-3/2x +24
C. y= 2/3x + 14
D. y= 2/3x + 8

Answers

Answer:

B. y = -3/2x + 24

Step-by-step explanation:

The perpendicular slope is -3/2x to find the y-intercept use the point given

Plug in

6 = -3/2(12) + b (b = y-intercept)

6 = -18 + b (add 18 on both sides)

24 = b (so)

y = -3/2x + 24

Help me find the slope of this problem ??

Answers

Slope is -3. Change in y over change in x. Y2-y1/x2-x1
(0,15) (2,9)
9-15/2-0= -6/2= -3

f(x) = x + 7, g(x) = x - 7
(a) (f + g)(x) =
(b) (f-g)(x)=
(c) (fg)(x)=
(d) (f/g)(x)=

Answers

a) 2x

b) 14

c) x^2 -49

d) -1

____ is 22 more than 88

Answers

Answer:

110

Step-by-step explanation:

88+22=110

The students can make 6 tickets from each sheet of paper. How many sheets of paper. How many sheets of paper are needed for 125 tickets?

Answers

Answer:

21 sheets of paper

Step-by-step explanation:

If its basically 6 tickets to a piece of paper then you just divide 125 tickets by 6 and get 20.833.... Then your round to the nearest sheet which is 21.

Hope this helps!

Answer:

Approx. 21 sheets of paper

Step-by-step explanation:

1 sheet of paper is used to make 6 tickets

6 tickets = 1 sheet

If 1 sheet is used to make 6 tickets. The number of sheets used to make 125 tickets will more.

if

6 tickets = 1 sheet

125 tickets = (125÷6) × 1

= 20.83333333333

can anyone help me ​

Answers

Answer:

A

Step-by-step explanation:

Claire wants to determine how her math score 690 on a standardized college entrance exam compared to her mother score 680 what she took the exam 20 years earlier the year Clair took the exam the mean math score was 510 with a standard deviation of 110 points on Claires mother took the exam the mean math score was 490 with a standard deviation of 100 points who has the better relative performance

Answers

Answer:

Claires mother did better because her z score was greater than Claires

Step-by-step explanation:

I j took the quiz

Claire's mother did better because her z-score was greater than that of Claires.

What is Z -score?

A Z-score is defined as the fractional representation of data point to the mean using standard deviations.

As per the given information, the solution would be as

Here is Claire's data:

ц₁ = 510

σ₁ = 110

X₁ = 690

⇒ z-score = (X₁-ц₁ )/σ₁

Substitute the values,

⇒ z-score = (690 - 510)/110

⇒ z-score = 180/110

⇒ z-score = 1.636

Here is Claire's mother's data:

ц = 490

σ₂ = 100

X₂ = 680

⇒ z-score = (X₂-ц )/σ₂

Substitute the values,

⇒ z-score = (680 - 490)/100

⇒ z-score = 190/100

⇒ z-score = 1.9

So Claire's mother's z-score > Claire's z-score

Therefore, Claire's mother did better because her z-score was greater than that of Claires.

Learn more about the z-score here:

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HELP! Will be giving branliest!!!!!!

Answers

A is the right anwer to your Question because of the Hours and weeks

I’m like pretty sure it’s B. h = w/e because it seems like you’re to find Toms hours worked which can be calculated by the hourly wages over what he earns.

MATH what is 9x1 9x2 9x3 9x4 9x5 9x6 9x7 9x8 9x9 9x10



EASY MATH 10 POINT

Answers

9 x 1 = 9
9 x 2 = 18
9 x 3 = 27
9 x 4 = 36
9 x 5 = 45
9 x 6 = 54
9 x 7 = 64
9 x 8 = 72
9 x 9 = 81
9 x 10 = 90

Answer:

9

18

27

36

45

54

63

72

81

90

Step-by-step explanation:

I just take the last numer of the times 9 and subtract 1 and put whatever equals 9.

example 9x7=63

7-1=6+3 so 63

Sorry if it does not make sense

−20=−4x−6x Find the value of x

Answers

Answer:

[tex]\huge\boxed{x=2}[/tex]

Step-by-step explanation:

[tex]-20=-4x-6x\qquad|\text{combine like terms}\\\\-20=-10x\qquad|\text{divide both sides by (-10)}\\\\\dfrac{-20}{-10}=\dfrac{-10x}{-10}\\\\2=x\to x=2[/tex]

The formula to put in E176 that will give me the sum of all the units sold by the indicated sales rep and product is:

Answers

Question attached

Answer :

There is no such formular

Explanation:

there is no such Formula I'm the options given. However the total product units sold by the sales representative for the period can be calculated in the excel sheet by adding up the cells with the units sold(cells F179,F180... to F186) and inserting the formula in the cell under total units sold by sales representative. So any change of figures in the cells added would reflect in the total units cell E176, if there is an additional figure for units sold in another cell, we could add this cell to formula in E176

what is 78756567.998 divided by 76454

Answers

Answer:

1,030.11703766971

Step-by-step explanation:

Just use a calculator (windows + r and then type calc if your on windows or search up calculator)

A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 8 ft, find the value of x so that the greatest possible amount of light is admitted.

Answers

Answer: x = 2

If x is the width of the window, the value for x that results in the greatest area-- presumably admitting the greatest amount of light.

Step-by-step explanation:

Initial calculations to find a starting value for w.

Determine dimensions that will have a sum of 8 as the perimeter. The length of the arc plus three sides of the rectangle.

The length of the arc is  half the circumference of the circle, the width is the diameter. So, modifying the equation: C= πd,  a = πw/2

Three sides of a rectangle (presumably a square for the initial calculation) 3w

Initial equation: 3w + πw/2 = 8    Substitute 3.14 for π  and solve for w

2(3w) + 2(3.14w/2) = 2(8)   multiply all terms by 2 to eliminate denominator

6w + 3.14w = 16   combine like terms

9.14w  = 16   divide both sides by 9.14

w ≈ 1.75

Calculate the area using this value:

Area of semicircle:  πr²/2   r= 1.75/2  

3.14(.875)²/2 ≈ 1.203

Area of rectangle  1.75 × 1.75 = 3.0625

Total Area with width 1.75  :  4.265 ft²

Increasing the width to 2

The length of the arc becomes 3.14   This is twice the area of the semicircle.

3.14/2 = 1.57

The height of the rectangle reduces to 1.43

1.43 × 2 = 2.86

Total area with width of 2 ft   2.86 + 1.57 = 4.43 ft²

So 2 ft seems to be the optimal width.

Write the equation of a line with slope 2 and y-intercept −1.
Answer:
y =

Answers

Answer: y = 2x - 1

Step-by-step explanation: The form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept. Just plug in the values, and you have your answer!

Carrie has $500 in her bank account. She plans to add $245 a week to her account. Jose has $710 in his bank account. He plans to add $230 a week. How many weeks will it take untill carrie & jose have an equal ammount of money saved up is neither of them spent any of their savings?

Answers

Answer:

14 weeks

Step-by-step explanation:

14 times 245= 3430+ 500=3930 (carrie)

14 times 230= 3220+ 710= 3930 (jose)

- 8n - 8 = -72
I don’t know how to do this

Answers

Answer:

n=8

Step-by-step explanation:

Add 8 to both sides of the equals sign, then bring down -8n, add -72+8, You'll get -64, lastly you divide -64 and -8, and you'll get your answer

Start by turning everything positive! 8n + 8 = 72.
Then, having the 8 as a positive number, subtract it from the left side. 8n = 64
In our final step, we divide 64 by 8 to find what n is, n= 8
To check your work you can plug it back into the original equation, be sure that both sides equal each other!

Let x be a continuous random variable that is normally distributed with a mean of 25 and a standard deviation of 6. Find the probability that x assumes a value between 29.0 and 55.0. Use Table IV in Appendix C to compute the probabilities. Round your answer to four decimal places.

Answers

Answer:

i think it is between 22 and 35

Step-by-step explanation:

I need to find the missing angle for this triangle

Answers

Answer:

44 degrees

Step-by-step explanation:

Because a right angle triangle if added all angles will=to 180 degrees

so 46+90=136

180-136=44

Answer:

44

Step-by-step explanation:

You add 46 to the 90 degree angle (right angle) and get 136. Then, because the angles of a triangle add up to 180 degrees all the time, you would do 180-136 and get 44.

8. Fay Teng's expenditures for the past 3 months were: August,
$1,735.50; September, $1,829.42; and October, $1,793.88.
What is her average monthly expenditure?
9. You use the utility company's budget plan for paying your
home heating bills. You pay $75 a month for 9 months. Your
actual bills are: September, $28.95; October, $16.15; November,
$68.46; December, $109.34; January, $115.26; February. $94.19;
March $75.66; April, $51.97; and May, $49.16. Compute the
average for the 9 months.
ght The McGraw-e Companies, Inc. All rights

Answers

=$75.66 all in all and $67.99 dollars

Walt multiples 25 times 16 using partial products what did walt do wrong

Answers

Answer:

first what the full question and if 25*16/2=200

Step-by-step explanation:

Susan's grandpa was fibbing again: "your grandma and I, together, we are over 150

Answers

This doesn’t make sense, please add additional context

what is -1(9)


Ignore theses it said it was too short

Answers

-9, apologies if I got this wrong

why is 1+1 = 2 and not 8? Why did someone came up with 2? How do you approach 2 from 1+1? Who even invented numbers? Why is math a thing? Why are we conditioned to know that 1+1 =2?

Answers

Wot- I wish I knew that

Which is true when you rent?
ОА.
You build equity in your house.
ОВ.
You are responsible for any repairs.
Ос.
You pay fewer up-front costs.

Answers

You are responsible for any repairs.

Solve for x.
x-4/5= -1/3

Answers

Answer:

x = 1 2/15

Step-by-step explanation:

30=Five-sixthsY solve for Y​

Answers

Given :-

A linear Question is given to us .

The equⁿ is [tex]\sf 30 = \dfrac{5}{6}y[/tex]

To Find :-

The value of y .

Solution:-

Taking the given equⁿ :

[tex]\bf \implies30=\dfrac{5}{6}y[/tex]

[tex]\bf \implies 30\times 6=5y[/tex]

[tex]\bf\implies y=\dfrac{\cancel{30}\times6}{\cancel5}[/tex]

[tex]\underline{\boxed{\red{\bf{\longmapsto \qquad y \qquad = \qquad 36 \qquad}}}}[/tex]

[tex]\boxed{\green{\bf\pink{\dag}\: Hence\:the\:value\:of\:y\:is\:36.}}[/tex]

Some rules :-

On transposing numbers or variables,

Plus changes to minus.Minus changes to plus .Multiply changes to divide.Divide changes to multiply.
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