Jay Abramson

Practice Test

1.

Convert $\frac{5 π}{6}$ radians to degrees.

2.

Convert $−620°$ to radians.

3.

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

4.

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

5.

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

6.

Find the angle between 0 and $2 π$ in radians that is coterminal with $- \frac{4 π}{7} .$

7.

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

8.

Draw the angle $- \frac{π}{6}$ 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 $A B C : \sin B = \frac{3}{4}, c = 12.$

11.

Find the missing sides of the triangle.

A right triangle with hypotenuse length of 9 and angle measure of 60 degrees.

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 $\sin \frac{π}{6} .$

14.

Compute sine of $240° .$

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 $\cot \frac{π}{4} .$

18.

Find the exact value of $\tan \frac{π}{3} .$

19.

Use reference angles to evaluate $\csc \frac{7 π}{4} .$

20.

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

21.

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

22.

If $cos t = \frac{\sqrt{3}}{2},$ find $cos (t - 2 π) .$

23.

Find the missing angle: $\cos (\frac{π}{6}) = \sin (___)$