# Trigonometry : Graphs, Asymptotes and Phase Shifts (13 Problems)

1. If sin(alpha)=1/5 where alpha is in quadrant II, find the remaining five trigonometric functions of alpha.

2. Given that sin(alpha)= -2/3 and cos(alpha)= -root5/3>0, find the remaining four trigonometric functions.

3. Sketch a graph of y=3cos(2theta+pi) using either transformations or the "5 key points" method. Be sure to label the key points throughout the stages if you use transformations.

4. Sketch a graph of y= -tan(theta-(pi/4)) using transformations. Be sure to label the key points and asymptotes throughout the stages.

5. Sketch a graph of y=2csc(2theta+pi) using transformations or the "5 key points" method using the sine function as a guide. Be sure to label the key points and asymptotes throughout the stages.

6. State the amplitude, range, period and phase-shift of y= -4sin(2x-pi)

8. Find the exact value of cos(inverse sin(-1/3))

9. Find the exact value of sec(inverse tan(1/2))

10. Solve: 2cos(theta)+root3=0

11. Find the exact value of sin105degrees

12. Find the exact value of cos(7pi/12)

13. Use the fact that if cos(alpha)=1/root5, 0<alpha<pi/2 and sin(beta)= -4/5,

-pi/2<beta<0

A) Find the exact value of sin(alpha-beta)

B) Find the exact value of sin(2alpha)

C) Find the exact value of cos(beta/2)

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#### Solution Summary

Graphs, Asymptotes and Phase Shifts are investigated. The solution is detailed and well presented.