# Transformations of Trig Functions Worksheet

Transformations of Trig Functions Worksheet
• Page 1
1.
Identify the equation for a cosine function of peroid 180°, after a phase shift 10° to the right.
 a. $y$ = cos [2($\theta$ - 10°)] b. $y$ = cos $\theta$ + 10° c. $y$ = cos $\theta$ - 10° d. $y$ = cos [2($\theta$ + 10°)]

2.
Identify the equation for a cosine function of peroid 45°, after a phase shift 60° to the left.
 a. $y$ = cos [3($\theta$ + 60°)] b. $y$ = cos [8($\theta$ + 60°)] c. $y$ = cos [3($\theta$ - 60°)] d. $y$ = cos [8($\theta$ - 60°)]

3.
Identify the equation for a sine function of peroid 45°, after a phase shift 35° to the left.
 a. $y$ = sin [4($\theta$ + 35°)] b. $y$ = sin [4($\theta$ - 35°)] c. $y$ = sin [8($\theta$ + 35°)] d. $y$ = sin [8($\theta$ - 35°)]

4.
Identify the equation for a sine function of peroid 90°, after a phase shift 50° to the left.
 a. $y$ = sin [0.75($\theta$ + 50°)] b. $y$ = sin [4($\theta$ - 50°)] c. $y$ = sin [0.75($\theta$ - 50°)] d. $y$ = sin [4($\theta$ + 50°)]

5.
A cosine graph with amplitude 4 and period 60° is translated 5 units down. Identify the equation of the graph after transformation.
 a. $y$ = 4cos 6$\theta$ - 5 b. $y$ = 6cos 4$\theta$ + 1 c. $y$ = 4cos $\theta$ + 6 d. $y$ = 6cos 4$\theta$ - 5

6.
A cosine graph with amplitude 4 and period 180° is translated 1 unit down. Identify the equation of the graph after transformation.
 a. $y$ = 4cos 2$\theta$ + 3 b. $y$ = 4cos 2$\theta$ - 1 c. $y$ = 2cos 4$\theta$ - 1 d. $y$ = 4cos 2$\theta$ + 1

7.
A sine graph with amplitude 1 and period 30° is translated 3 units up. Identify the equation of the graph after transformation.
 a. $y$ = sin 8$\theta$ + 4 b. $y$ = sin 12$\theta$ + 3 c. $y$ = sin 3$\theta$ + 12 d. $y$ = sin 12$\theta$ - 3

8.
Identify the equation for a cosine function of peroid 180°, after a phase shift 10° to the right.
 a. $y$ = cos [2($\theta$ - 10°)] b. $y$ = cos [2($\theta$ + 10°)] c. $y$ = cos $\theta$ - 10° d. $y$ = cos $\theta$ + 10°

9.
Identify the equation for a cosine function of peroid 45°, after a phase shift 60° to the left.
 a. $y$ = cos [8($\theta$ + 60°)] b. $y$ = cos [3($\theta$ - 60°)] c. $y$ = cos [3($\theta$ + 60°)] d. $y$ = cos [8($\theta$ - 60°)]

 a. $y$ = sin [4($\theta$ - 35°)] b. $y$ = sin [8($\theta$ - 35°)] c. $y$ = sin [8($\theta$ + 35°)] d. $y$ = sin [4($\theta$ + 35°)]