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Find the area of the sector of a circle with diameter 32 feet and an angle of 3 π 5 radians.

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For the following exercises, find the angle between and 360° that is coterminal with the given angle.

For the following exercises, find the angle between 0 and 2 π in radians that is coterminal with the given angle.

20 π 11

2 π 11

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For the following exercises, draw the angle provided in standard position on the Cartesian plane.

Find the linear speed of a point on the equator of the earth if the earth has a radius of 3,960 miles and the earth rotates on its axis every 24 hours. Express answer in miles per hour. Round to the nearest hundredth.

1036.73 miles per hour

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A car wheel with a diameter of 18 inches spins at the rate of 10 revolutions per second. What is the car's speed in miles per hour? Round to the nearest hundredth.

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Right Triangle Trigonometry

For the following exercises, use side lengths to evaluate.

cos ( π 2 ) = sin ( ___° )

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csc ( 18° ) = sec ( ___° )

72°

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For the following exercises, use the given information to find the lengths of the other two sides of the right triangle.

tan A = 5 9 , b = 6

a = 10 3 , c = 2 106 3

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For the following exercises, use [link] to evaluate each trigonometric function.

A right triangle with side lengths of 11 and 6. Corners A and B are also labeled.  The angle A is opposite the side labeled 11.  The angle B is opposite the side labeled 6.

For the following exercises, solve for the unknown sides of the given triangle.

A 15-ft ladder leans against a building so that the angle between the ground and the ladder is 70° . How high does the ladder reach up the side of the building? Find the answer to four decimal places.

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The angle of elevation to the top of a building in Baltimore is found to be 4 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building. Find the answer to four decimal places.

369.2136 ft

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Unit Circle

Find the exact value of sin π 3 .

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Find the exact value of cos π 4 .

2 2

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Find the exact value of cos π .

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State the reference angle for 300° .

60°

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State the reference angle for 3 π 4 .

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Compute cosine of 330° .

3 2

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Compute sine of 5 π 4 .

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State the domain of the sine and cosine functions.

all real numbers

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State the range of the sine and cosine functions.

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The Other Trigonometric Functions

For the following exercises, find the exact value of the given expression.

For the following exercises, use reference angles to evaluate the given expression.

If sec ( t ) = −2.5 , what is the sec ( t ) ?

–2.5

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If tan ( t ) = −0.6 , what is the tan ( t ) ?

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If tan ( t ) = 1 3 , find tan ( t π ) .

1 3

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If cos ( t ) = 2 2 , find sin ( t + 2 π ) .

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Which trigonometric functions are even?

cosine, secant

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Which trigonometric functions are odd?

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Chapter practice test

Convert 5 π 6 radians to degrees.

150°

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Convert −620° to radians.

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Find the length of a circular arc with a radius 12 centimeters subtended by the central angle of 30° .

6.283 centimeters

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Find the area of the sector with radius of 8 feet and an angle of 5 π 4 radians.

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Find the angle between and 360° that is coterminal with 375° .

15°

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Find the angle between 0 and 2 π in radians that is coterminal with 4 π 7 .

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Draw the angle 315° in standard position on the Cartesian plane.


This is an image of a graph of a circle with an angle inscribed.

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Draw the angle π 6 in standard position on the Cartesian plane.

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A carnival has a Ferris wheel with a diameter of 80 feet. The time for the Ferris wheel to make one revolution is 75 seconds. What is the linear speed in feet per second of a point on the Ferris wheel? What is the angular speed in radians per second?

3.351 feet per second, 2 π 75 radians per second

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Find the missing sides of the triangle A B C : sin B = 3 4 , c = 12.

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Find the missing sides of the triangle.


A right triangle with hypotenuse length of 9 and angle measure of 60 degrees.

a = 9 2 , b = 9 3 2

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The angle of elevation to the top of a building in Chicago is found to be 9 degrees from the ground at a distance of 2000 feet from the base of the building. Using this information, find the height of the building.

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Find the exact value of sin π 6 .

1 2

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Compute sine of 240° .

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State the domain of the sine and cosine functions.

real numbers

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State the range of the sine and cosine functions.

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Find the exact value of cot π 4 .

1

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Find the exact value of tan π 3 .

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Use reference angles to evaluate csc 7 π 4 .

2

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Use reference angles to evaluate tan 210° .

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If csc t = 0.68 , what is the csc ( t ) ?

–0.68

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If cos t = 3 2 , find cos ( t 2 π ) .

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Find the missing angle: cos ( π 6 ) = sin ( ___ )

π 3

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Questions & Answers

x exposant 4 + 4 x exposant 3 + 8 exposant 2 + 4 x + 1 = 0
HERVE Reply
x exposent4+4x exposent3+8x exposent2+4x+1=0
HERVE
How can I solve for a domain and a codomains in a given function?
Oliver Reply
ranges
EDWIN
Thank you I mean range sir.
Oliver
proof for set theory
Kwesi Reply
don't you know?
Inkoom
find to nearest one decimal place of centimeter the length of an arc of circle of radius length 12.5cm and subtending of centeral angle 1.6rad
Martina Reply
factoring polynomial
Noven Reply
what's your topic about?
Shin Reply
find general solution of the Tanx=-1/root3,secx=2/root3
Nani Reply
find general solution of the following equation
Nani
the value of 2 sin square 60 Cos 60
Sanjay Reply
0.75
Lynne
0.75
Inkoom
when can I use sin, cos tan in a giving question
duru Reply
depending on the question
Nicholas
I am a carpenter and I have to cut and assemble a conventional roof line for a new home. The dimensions are: width 30'6" length 40'6". I want a 6 and 12 pitch. The roof is a full hip construction. Give me the L,W and height of rafters for the hip, hip jacks also the length of common jacks.
John
I want to learn the calculations
Koru Reply
where can I get indices
Kojo Reply
I need matrices
Nasasira
hi
Raihany
Hi
Solomon
need help
Raihany
maybe provide us videos
Nasasira
about complex fraction
Raihany
Hello
Cromwell
a
Amie
What do you mean by a
Cromwell
nothing. I accidentally press it
Amie
you guys know any app with matrices?
Khay
Ok
Cromwell
Solve the x? x=18+(24-3)=72
Leizel Reply
x-39=72 x=111
Suraj
Solve the formula for the indicated variable P=b+4a+2c, for b
Deadra Reply
Need help with this question please
Deadra
b=-4ac-2c+P
Denisse
b=p-4a-2c
Suddhen
b= p - 4a - 2c
Snr
p=2(2a+C)+b
Suraj
b=p-2(2a+c)
Tapiwa
P=4a+b+2C
COLEMAN
b=P-4a-2c
COLEMAN
like Deadra, show me the step by step order of operation to alive for b
John
A laser rangefinder is locked on a comet approaching Earth. The distance g(x), in kilometers, of the comet after x days, for x in the interval 0 to 30 days, is given by g(x)=250,000csc(π30x). Graph g(x) on the interval [0, 35]. Evaluate g(5)  and interpret the information. What is the minimum distance between the comet and Earth? When does this occur? To which constant in the equation does this correspond? Find and discuss the meaning of any vertical asymptotes.
Kaitlyn Reply
The sequence is {1,-1,1-1.....} has
amit Reply
Practice Key Terms 6

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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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