1. Consider an Object Moving on a Circular Path with a Radius of 4.2 Meters

Mid-Mod 7/Unit Circle Test Review

Complete the following WITH a calculator.

1. Consider an object moving on a circular path with a radius of 4.2 meters. a. How many degrees are swept out when the object travels 19 meters on the circular path? 5 b. How many meters does the object travel when it sweeps out radians on the circular 9 path? c. What does it mean for the object to travel 2.5 radians? d. Suppose the distance the object traveled on the circular path varied from 3.2 meters to 8.3 meters. How many radians did the object sweep out over this distance? e. If the circle’s center is placed at the point (0,0) and object stopped at the point (3.67, -1.28), how many radians did the object travel?

2. Find the exact values of the six trig functions of . Sketch the angle in standard position. 5 sin  =  ;  in Quad 3 cos  = sec = 13 sin = csc =

tan = cot =

3. Express each angle in degrees. 7 11 a. b.  c. 2.4 3 30

4. Express each angle in radians. (Reduce and leave in terms of ) a. 320 b. 144 c. -75

5. Find the degree measure of the central angle associated with:

a. An arc that is 14.5 cm in a circle with a diameter of 8 cm. b. An arc that is 20.2 cm in a circle with a radius of 4 cm.

Complete the following WITHOUT a calculator.

6. Find the exact value of each trigonometric function.

 2  11 5 a. csc  b. sin c. tan  3  6 4

2  5  d. cos e. sec  f. cot 5  3  3  7. Find all solutions in radians. 3 2 3 a. 2  sec b. tan   c. csc   3 3 1 2 d.   sin  e. cot   DNE f.  cos 2 2

3 1 g. 2  2sin   4 h.  3  4 tan   7 i.  1 csc 2 2

8. Find the principal values of the following.

2 1 a. sin   b. cot    3 c. cos   2 2

d. tan   1 e. sec  1 f. csc  0

9. Evaluate.

  3 3   1   1 1  a. tan Sin 1  b. sin Sin  Tan   4   2 3 

  3    1 7    1 1   c. cscArc tan   Sin 1 d. cotCos       3     2  3 

 4   5 1 e. Cos 1 sin  f. cos   Sin 1  3   6 2

 1  10. Sketch the graph of g( )  2.5sin   , where x is in radians on the interval  3    3  2  a. What is the maximum of g? For what value(s) of x does g assume its maximum? b. Identify the root(s) and vertical intercept of g. c. Identify the period of g on the graph.  d. Describe how the output values of g vary as the input values vary from to  . 2 e. What is the amplitude of g?

** Be familiar with how to graph arcsine, arccosine, and arctangent **