Name ___________________________________________________ Date ________________ Period _______ Test 11 Review Ms. Williams

Trigonometry Graphs Review

Part I: Multiple Choice. Write the number of the best choice on the line provided. _______ 1. What is the equation for the accompanying graph? (1)

y cos2x (3)

y 2cosx

(2)

y 1

2cosx (4)

y cos1

2x

_______ 2. What is the period of the graph whose equation is

y 3cos2x?

(1) 180° (2) 2 (3) 3 (4) 360°

_______ 3. What is the range of the function

y 5sinx?

(1) 0° ≤ x ≤ 360° (3) -1 ≤ y ≤ 1 (2) 0° ≤ y ≤ 360° (4) -5 ≤ y ≤ 5

_______ 4. Which function has the same period as

y 4cos2x?

(1)

y 4cosx (2)

y 4sinx (3)

y tanx (4)

y tan2x

_______ 5. What is the equation for the accompanying graph? (1)

y 3sin3x

(2)

y 3sinx

(3)

y sin3x

(4)

y sin1

3x

_______ 6. What is the amplitude of the graph of the equation

y 3cos2x?

(1) 1 (2) 2 (3) 3 (4) 180

_______ 7. What is the minimum value in the range of

y 2sinx 3?

(1) 1 (2) 0 (3) -1 (4) -5

_______ 8. For which value of θ is

tan undefined?

(1) 0 (2)

2 (3) π (4) It is never undefined.

Part II: Graphing. For each question in this section, make a table of values and graph the equations. Answer any questions that follow. 9. Graph the equation

y 2sinx 1 in the interval - ≤ x ≤ .

Show work here! 10. Graph the equation xy 2cos in the interval 0 ≤ x ≤ 2π.

Show work here!

11. a) On the same set of axes, graph the equations

y sin1

2x and

y 3cosx in the

interval 0 ≤ x ≤ 2π b) Use the graph from part a to determine how many values of x in the given interval

are solutions to the equation

sin1

2x 3cosx

Show work here!

12. a) On the same set of axes, graph the equations xy tan and

y 1

2cosx in the

interval -2π ≤ x ≤ 2π b) Use the graph from part a to determine how many values of x in the given interval

are solutions to the equation xx 2cos2

1tan

Show work here!

Part III: For each equation, determine the amplitude, range, frequency, and period.

13. xy 5sin2 14.

y 17cosx 15.

y 4sin2

3x

Part IV: Identifying equations of trig graphs. Write an equation for each graph. 16. 17. 18. 19.

Part IV:

Part V: Writing equations of phase shifts.