Trig Graph → Cosine Graphs: Mixed Practice

1) Which equation has amplitude 1 and period π for a sine graph?

Y = sin(x/2)

Y = sin(x) + 1

Y = sin(2x)

Y = 2sin(x)

2) What is the phase shift of y = cos(x - π/3)?

Left π/3

Right π/3

None

Right π/6

3) Which equation matches a cosine graph with amplitude 2, period π/2, midline y = 0, and a minimum at x = 0?

Y = 2cos(4x)

Y = -2cos(4x)

Y = 2cos(x/4)

Y = -2cos(x/4)

4) What is the period of y = sin(0.5x)?

4π

2π

π/2

π

5) Which function has amplitude 1/3?

Y = cos(x/3)

Y = 3cos(x)

Y = (1/3)cos(5x)

Y = cos(5x) + 1/3

6) What is the midline of y = -7cos(x) + 3?

Y = -7

Y = -3

Y = 0

Y = 3

7) The graph of y = -(1/2)cos(6x) has which amplitude and period?

Amplitude 2, period π/3

Amplitude 1/2, period π/3

Amplitude 1/2, period 6π

Amplitude 1, period 2π

8) What is the period of y = sin(3(x - π/4))?

π/3

3π

2π

2π/3

9) What is the amplitude of y = √2 sin(x)?

2

1

√2

1/√2

10) Which of the following equations matches a sine graph with amplitude 4 and period π?

Y = 4sin(x/2)

Y = sin(4x)

Y = 4sin(2x)

Y = 2sin(4x)

11) Which equation matches amplitude 2 and period 4π with midline y = 0?

Y = 2cos(x/2)

Y = 2cos(2x)

Y = cos(x/2)

Y = (1/2)cos(2x)

12) The graph of y = 2cos(3x) has which amplitude and period?

Amplitude 3, period 2π

Amplitude 2, period 2π/3

Amplitude 1, period 3π

Amplitude 2, period 3π

13) What is the amplitude of y = -(3/2)sin(5x)?

-3/2

5

2/3

3/2

14) Which equation matches a cosine graph with amplitude 5, period 2π, midline y = -4, and a maximum at x = 0?

Y = 5cos(x) - 4

Y = 5cos(2x) - 4

Y = cos(5x) - 4

Y = 5cos(x) + 4

15) What is the period of y = cos(x/5)?

5π

10π

2π/5

2π

16) Which equation has amplitude 1 and midline y = -3?

Y = cos(x) - 3

Y = -3cos(x)

Y = cos(x) + 3

Y = 3cos(x) - 1

17) What is the midline of y = -5cos(x) + 2?

Y = 2

Y = -2

Y = 0

Y = 5

18) The graph of y = sin(x/4) has which amplitude and period?

Amplitude 4, period 2π

Amplitude 1, period 4π

Amplitude 1, period 8π

Amplitude 1/4, period 2π

19) Which function has a maximum at x = 0?

Y = -sin(x)

Y = sin(x)

Y = -cos(x)

Y = cos(x)

20) What is the phase shift of y = sin(x + π/6)?