Algebra and Trigonometry

# Review Exercises

Algebra and TrigonometryReview Exercises

#### Angles

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

1.

2.

$− 5π 3 − 5π 3$

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

3.

$−210° −210°$

4.

$180° 180°$

5.

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

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$0° 0°$and$360° 360°$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.

$−210° −210°$

12.

$75° 75°$

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. Round to the nearest hundredth.

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? Round to the nearest hundredth.

#### Right Triangle Trigonometry

For the following exercises, use side lengths to evaluate.

17.

$cos π 4 cos π 4$

18.

$cot π 3 cot π 3$

19.

$tan π 6 tan π 6$

20.

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

21.

$csc( 18° )=sec( ___° ) csc( 18° )=sec( ___° )$

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

22.

$cos B= 3 5 ,a=6 cos B= 3 5 ,a=6$

23.

$tan A= 5 9 ,b=6 tan A= 5 9 ,b=6$

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

Figure 1
24.

25.

$tan B tan B$

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

26. 27. 28.

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? Find the answer to four decimal places.

29.

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.

#### Unit Circle

30.

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

31.

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

32.

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

33.

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

34.

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

35.

Compute cosine of$330°. 330°.$

36.

Compute sine of$5π 4 . 5π 4 .$

37.

State the domain of the sine and cosine functions.

38.

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.

39.

$cos π 6 cos π 6$

40.

$tan π 4 tan π 4$

41.

$csc π 3 csc π 3$

42.

$sec π 4 sec π 4$

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

43.

$sec 11π 3 sec 11π 3$

44.

$sec 315° sec 315°$

45.

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

46.

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

47.

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

48.

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

49.

Which trigonometric functions are even?

50.

Which trigonometric functions are odd?