Precalculus 2e

# Review Exercises

Precalculus 2eReview Exercises

### Review Exercises

##### Angles

For the following exercises, convert the angle measures to degrees.

1.

$π 4 π 4$

2.

$− 5π 3 − 5π 3$

For the following exercises, convert the angle measures to radians.

3.

-210°

4.

180°

5.

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

6.

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

For the following exercises, find the angle between 0° and 360° that is coterminal with the given angle.

7.

$420° 420°$

8.

$−80° −80°$

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

9.

$− 20π 11 − 20π 11$

10.

$14π 5 14π 5$

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

11.

-210°

12.

75°

13.

$5π 4 5π 4$

14.

$− π 3 − π 3$

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.

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?

##### Unit Circle: Sine and Cosine Functions
17.

Find the exact value of $sin π 3 . sin π 3 .$

18.

Find the exact value of $cos π 4 . cos π 4 .$

19.

Find the exact value of $cosπ. cosπ.$

20.

State the reference angle for $300°. 300°.$

21.

State the reference angle for $3π 4 . 3π 4 .$

22.

Compute cosine of $330°. 330°.$

23.

Compute sine of $5π 4 . 5π 4 .$

24.

State the domain of the sine and cosine functions.

25.

State the range of the sine and cosine functions.

##### The Other Trigonometric Functions

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

26.

$cos π 6 cos π 6$

27.

$tan π 4 tan π 4$

28.

$csc π 3 csc π 3$

29.

$sec π 4 sec π 4$

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

30.

$sec 11π 3 sec 11π 3$

31.

$sec315° sec315°$

32.

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

33.

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

34.

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

35.

If $cos(t)= 2 2 , cos(t)= 2 2 ,$ find $sin(t+2π). sin(t+2π).$ There are two possible solutions.

36.

Which trigonometric functions are even?

37.

Which trigonometric functions are odd?

##### Right Triangle Trigonometry

For the following exercises, use side lengths to evaluate.

38.

$cos π 4 cos π 4$

39.

$cot π 3 cot π 3$

40.

$tan π 6 tan π 6$

41.

$cos( π 2 )=sin(__°) cos( π 2 )=sin(__°)$

42.

$csc(18°)=sec(__°) csc(18°)=sec(__°)$

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

43.

$cosB= 3 5 ,a=6 cosB= 3 5 ,a=6$

44.

$tanA= 5 9 ,b=6 tanA= 5 9 ,b=6$

For the following exercises, use Figure 1 to evaluate each trigonometric function.

Figure 1
45.

$sinA sinA$

46.

$tanB tanB$

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

47. 48. 49.

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

50.

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. Do you know how you learn best?