Assignment #1
DUE by 6/9/02
1. Find the radian measure of a central angle θ opposite an arc measure 16 inches in a
circle of radius 8 inches.
2. Find the exact radian measure, in terms of π, of each angle.
a.  90
b. 180
c.  270
3. Find the exact degree measure of each angle.



a.
b.
c.
6
3
2
4. Determine which quadrant the angle
d.
d.  360
5
6
8
, in standard position, lies in.
3
5. Determine the radian measure for a 2/9 rotation.
6. Given triangle ABC with right angle C with opposite sides a, b, and c, respectively.
Find the missing sides and angles to 3 significant digits given B = 33.7 , b = 22.4.
7. Determine whether the statement is true or false. If true, explain why. If false, give a
counterexample. Let A and B be acute angles. If A < B, then cot A < cot B.
8. Explain what happens to each of the following as the acute angle θ approaches 90 :
a. sin θ
b. tan θ
c. csc θ
9. Find the value of each of the other five trigonometric functions for an angle  (without
5
finding ) given csc    with  being an angle in quadrant III.
4
10. Using a calculator, evaluate to 4 significant digits: cot 25.1 rad
11. Find the exact values of each of the six trigonometric functions for an angle  whose
terminal side is at (1,  3 ) .
12. Given cos  0 , determine the quadrants in which the terminal side of an angle 
must lie in.
13. Find the exact value of each of the other five trigonometric functions for an angle 
2
(without finding ) given sin    with angle  located in quadrant III.
3
14. Use right triangle trig ratios to evaluate cot 30. Do not use a calculator or table.
Leave answers involving radicals in exact radical form.
 2 
15. Use right triangle trig ratios to evaluate csc 
 . Do not use a calculator or table.
 3 
Leave answers involving radicals in exact radical form.
16. Find the smallest positive  in degree measure for which csc  = -2.
17. Find exactly all , 0  θ < 360º, for which cot   
1
3
.
18. Using unit circle, find the coordinates of the circular point P for x 
x
3
.
2
19. Find the exact values of x when cos x  
1
2
,  2  x  2 .
20. Evaluate sec (45) to 4 significant digits using a calculator.
21. If sin x = -0.1377, find sin (x + 2π).

and for
2