Algebra and Trigonometry

# Review Exercises

Algebra and TrigonometryReview 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.

$−210° −210°$

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.

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

23.

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

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

Figure 1
24.

$sinA sinA$

25.

$tanB tanB$

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 $cosπ. cosπ.$

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.

$sec315° sec315°$

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? Do you know how you learn best?
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