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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

write down the polynomial function with root 1/3,2,-3 with solution
Gift Reply
if A and B are subspaces of V prove that (A+B)/B=A/(A-B)
Pream Reply
write down the value of each of the following in surd form a)cos(-65°) b)sin(-180°)c)tan(225°)d)tan(135°)
Oroke Reply
Prove that (sinA/1-cosA - 1-cosA/sinA) (cosA/1-sinA - 1-sinA/cosA) = 4
kiruba Reply
what is the answer to dividing negative index
Morosi Reply
In a triangle ABC prove that. (b+c)cosA+(c+a)cosB+(a+b)cisC=a+b+c.
Shivam Reply
give me the waec 2019 questions
Aaron Reply
the polar co-ordinate of the point (-1, -1)
Sumit Reply
prove the identites sin x ( 1+ tan x )+ cos x ( 1+ cot x )= sec x + cosec x
Rockstar Reply
tanh`(x-iy) =A+iB, find A and B
Pankaj Reply
B=Ai-itan(hx-hiy)
Rukmini
what is the addition of 101011 with 101010
Branded Reply
If those numbers are binary, it's 1010101. If they are base 10, it's 202021.
Jack
extra power 4 minus 5 x cube + 7 x square minus 5 x + 1 equal to zero
archana Reply
the gradient function of a curve is 2x+4 and the curve passes through point (1,4) find the equation of the curve
Kc Reply
1+cos²A/cos²A=2cosec²A-1
Ramesh Reply
test for convergence the series 1+x/2+2!/9x3
success 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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