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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

sinx sin2x is linearly dependent
cr Reply
what is a reciprocal
Ajibola Reply
The reciprocal of a number is 1 divided by a number. eg the reciprocal of 10 is 1/10 which is 0.1
Shemmy
 Reciprocal is a pair of numbers that, when multiplied together, equal to 1. Example; the reciprocal of 3 is ⅓, because 3 multiplied by ⅓ is equal to 1
Jeza
each term in a sequence below is five times the previous term what is the eighth term in the sequence
Funmilola Reply
I don't understand how radicals works pls
Kenny Reply
How look for the general solution of a trig function
collins Reply
stock therom F=(x2+y2) i-2xy J jaha x=a y=o y=b
Saurabh Reply
sinx sin2x is linearly dependent
cr
root under 3-root under 2 by 5 y square
Himanshu Reply
The sum of the first n terms of a certain series is 2^n-1, Show that , this series is Geometric and Find the formula of the n^th
amani Reply
cosA\1+sinA=secA-tanA
Aasik Reply
Wrong question
Saad
why two x + seven is equal to nineteen.
Kingsley Reply
The numbers cannot be combined with the x
Othman
2x + 7 =19
humberto
2x +7=19. 2x=19 - 7 2x=12 x=6
Yvonne
because x is 6
SAIDI
what is the best practice that will address the issue on this topic? anyone who can help me. i'm working on my action research.
Melanie Reply
simplify each radical by removing as many factors as possible (a) √75
Jason Reply
how is infinity bidder from undefined?
Karl Reply
what is the value of x in 4x-2+3
Vishal Reply
give the complete question
Shanky
4x=3-2 4x=1 x=1+4 x=5 5x
Olaiya
hi can you give another equation I'd like to solve it
Daniel
what is the value of x in 4x-2+3
Olaiya
if 4x-2+3 = 0 then 4x = 2-3 4x = -1 x = -(1÷4) is the answer.
Jacob
4x-2+3 4x=-3+2 4×=-1 4×/4=-1/4
LUTHO
then x=-1/4
LUTHO
4x-2+3 4x=-3+2 4x=-1 4x÷4=-1÷4 x=-1÷4
LUTHO
A research student is working with a culture of bacteria that doubles in size every twenty minutes. The initial population count was  1350  bacteria. Rounding to five significant digits, write an exponential equation representing this situation. To the nearest whole number, what is the population size after  3  hours?
David Reply
f(x)= 1350. 2^(t/20); where t is in hours.
Merkeb
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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