Trigonometry – Precalculus
Evaluate.
1. Give the degree measure of   cot 1  1 . Do not use a calculator.
2. Find the amplitude, the period, any vertical translation, and any phase shift of the graph of

1
y  3cos  x  
6
2
3. Find the exact value of cos  , give that sin   
4
and tan   0 .
5
4. Find the exact value of tan  , give that sin   
1
and  is in quadrant III.
2
Graph the trigonometry functions.
5. Graph y  3cos  2 x  .
6. Graph one period of y  sin  x    .
Solve each equation for exact solutions over the interval 0, 2  .
7. cos   1  0
8. tan x  cot x
9. sec2 2 x  2
10. 3sin 2 x  5sin x  2  0
11. cos 2 x  cos x  0
Evaluate.


12. Express cos 270  x as a function of x alone.
13. Express tan   x  as a function of x alone.
Find the centers, radii and equations of circles.
14. Find the center and radius of  x  4   y  1  16 and then graph it.
2
2
15. Write the equation of the circle with radius 9 and center at  2, 5  .
Answer key
1.   135
2. Amplitude = 3 , Period = 12 , Vertical translation = 0 , Phase shift =
3.
4.
3
5
3
3
5.
6.
7.    , 3
8. x 
9. x 
 3 5 7
4
,
4
,
4
,
4
 3 5 7 9 11 13 15
8
10. x 
11. x 
,
8
,
8

,
8
,
8
,
8
,
2
2
, sin 1   ,   sin 1  
2
3
3
 5
, ,
3 3
12.  sin x
8
,
8
1
2
13. tan x
14. Center =  4, 1 ; Radius = 4
15.  x  2   y  5  81
2
2