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5.R: Trigonometric Functions (Review)

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5.1: Review Exercises

For the exercises 1-2, convert the angle measures to degrees.

1) π4

Answer

45°

2) −\dfrac{5π}{3}

For the exercises 3-6, convert the angle measures to radians.

3) -210°

Answer

−\dfrac{7π}{6}

4) 180°

5) Find the length of an arc in a circle of radius 7 meters subtended by the central angle of 85°.

Answer

10.385 meters

6) Find the area of the sector of a circle with diameter 32 feet and an angle of \dfrac{3π}{5} radians.

For the exercises 7-8, find the angle between and 360° that is coterminal with the given angle.

7) 420°

Answer

60°

8) −80°

For the exercises 9-10, find the angle between 0 and in radians that is coterminal with the given angle.

9) − \dfrac{20π}{11}

Answer

\dfrac{2π}{11}

10) \dfrac{14π}{5}

For the exercises 11-, draw the angle provided in standard position on the Cartesian plane.

11) -210°

Answer

alt

12) 75°

13) \dfrac{5π}{4}

Answer

CNX_Precalc_Figure_05_04_219.jpg

14) −\dfrac{π}{3}

15) 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.

Answer

1036.73 miles per hour

16) 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?

5.2: Review Exercises

1) Find the exact value of \sin \dfrac{π}{3}.

Answer

\dfrac{\sqrt{3}}{2}

2) Find the exact value of \cos \dfrac{π}{4}.

3) Find the exact value of \cos π .

Answer

-1

4) State the reference angle for 300°.

5) State the reference angle for \dfrac{3π}{4}.

Answer

\dfrac{π}{4}

6) Compute cosine of 330°.

7) Compute sine of \dfrac{5π}{4}.

Answer

−\dfrac{\sqrt{2}}{2}

8) State the domain of the sine and cosine functions.

9) State the range of the sine and cosine functions.

Answer

[–1,1]

5.3: Review Exercises

For the exercises 1-4, find the exact value of the given expression.

1) \cos \dfrac{π}{6}

2) \tan \dfrac{π}{4}

Answer

1

3) \csc \dfrac{π}{3}

4) \sec \dfrac{π}{4}

Answer

\sqrt{2}

For the exercises 4-12, use reference angles to evaluate the given expression.

5) \sec \dfrac{11π}{3}

6) \sec 315°

Answer

\sqrt{2}

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

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

Answer

0.6

9) If \tan (t)=\dfrac{1}{3}, find \tan (t−π).

10) If \cos (t)= \dfrac{\sqrt{2}}{2}, find \sin (t+2π).

Answer

\dfrac{\sqrt{2}}{2} or −\dfrac{\sqrt{2}}{2}

11) Which trigonometric functions are even?

12) Which trigonometric functions are odd?

Answer

sine, cosecant, tangent, cotangent

5.4: Review Exercises

For the exercises 1-5, use side lengths to evaluate.

1) \cos \dfrac{π}{4}

2) \cot \dfrac{π}{3}

Answer

\dfrac{\sqrt{3}}{3}

3) \tan \dfrac{π}{6}

4) \cos (\dfrac{π}{2}) = \sin ( \_\_°)

Answer

0

5) \csc (18°)= \sec (\_\_°)

For the exercises 6-7, use the given information to find the lengths of the other two sides of the right triangle.

6) \cos B= \dfrac{3}{5}, a=6

Answer

b=8,c=10

7) \tan A = \dfrac{5}{9},b=6

For the exercises 8-9, use Figure below to evaluate each trigonometric function.

alt

8) \sin A

Answer

\dfrac{11\sqrt{157}}{157}

9) \tan B

For the exercises 10-11, solve for the unknown sides of the given triangle.

10)

alt

Answer

a=4, b=4

11)

alt

12) 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?

Answer

14.0954 ft

13) 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.

Practice Test

1) Convert \dfrac{5π}{6} radians to degrees.

Answer

150°

2) Convert −620° to radians.

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

Answer

6.283 centimeters

4) Find the area of the sector with radius of 8 feet and an angle of \dfrac{5π}{4} radians.

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

Answer

15°

6) Find the angle between 0 and in radians that is coterminal with −\dfrac{4π}{7}.

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

Answer

alt

8) Draw the angle −\dfrac{π}{6} in standard position on the Cartesian plane.

9) 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?

Answer

3.351 feet per second, \dfrac{2π}{75} radians per second

10) Find the exact value of \sin \dfrac{π}{6}.

11) Compute sine of 240°.

Answer

−\dfrac{\sqrt{3}}{2}

12) State the domain of the sine and cosine functions.

13) State the range of the sine and cosine functions.

Answer

[ –1,1 ]

14) Find the exact value of \cot \dfrac{π}{4}.

15) Find the exact value of \tan \dfrac{π}{3}.

Answer

\sqrt{3}

16) Use reference angles to evaluate \csc \dfrac{7π}{4}.

17) Use reference angles to evaluate \tan 210°.

Answer

\dfrac{\sqrt{3}}{3}

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

19) If \cos t= \dfrac{\sqrt{3}}{2}, find \cos (t−2π).

Answer

\dfrac{\sqrt{3}}{2}

20) Which trigonometric functions are even?

21) Find the missing angle: \cos \left(\dfrac{\pi }{6} \right)= \sin (\;)

Answer

\dfrac{π}{3}

22) Find the missing sides of the triangle ABC: \sin B= \dfrac{3}{4},c=12

23) Find the missing sides of the triangle.

alt

Answer

a=\dfrac{9}{2},b=\dfrac{9\sqrt{3}}{2}

24) 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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