Algebra and Trigonometry

# Practice Test

1.

Convert$5π 6 5π 6$radians to degrees.

2.

Convert$−620° −620°$to radians.

3.

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

4.

Find the area of the sector with radius of 8 feet and an angle of$5π 4 5π 4$ radians.

5.

Find the angle between$0° 0°$and$360° 360°$ that is coterminal with$375°. 375°.$

6.

Find the angle between 0 and$2π 2π$in radians that is coterminal with$− 4π 7 . − 4π 7 .$

7.

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

8.

Draw the angle$− π 6 − π 6$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?

10.

Find the missing sides of the triangle$ABC:sin B= 3 4 ,c=12. ABC:sin B= 3 4 ,c=12.$

11.

Find the missing sides of the triangle. 12.

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.

13.

Find the exact value of$sin π 6 . sin π 6 .$

14.

Compute sine of$240°. 240°.$

15.

State the domain of the sine and cosine functions.

16.

State the range of the sine and cosine functions.

17.

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

18.

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

19.

Use reference angles to evaluate$csc 7π 4 . csc 7π 4 .$

20.

Use reference angles to evaluate$tan 210°. tan 210°.$

21.

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

22.

If$cos t= 3 2 , cos t= 3 2 ,$find$cos(t−2π). cos(t−2π).$

23.

Find the missing angle:$cos( π 6 )=sin( ___ ) cos( π 6 )=sin( ___ )$