Model Periodic Phenomena with Trigonometric Functions

1) Which function has no amplitude?

Y = tan(0.2x)

Y = -5 sin(x)

Y = 3 cos(x)

Y = (1/2) sin(x)

2) Which cosine function has amplitude 1, period 2π, and is reflected across the x-axis?

Y = cos(x)

Y = -cos(x)

Y = -cos(2x)

Y = -2cos(x)

3) What is the period of y = sec(2.5x - π)?

4π/5

5π/2

2π/5

5π

4) What is the domain of y = csc(2x)?

All real x except x = kπ

All real x

All real x except x = kπ/2

All real x except x = π/4 + kπ/2

5) Which equation matches a sine graph with amplitude 3, period 4π, and midline y = 0?

Y = 3sin(2x)

Y = 3sin(x/2)

Y = sin(3x/2)

Y = 3sin(x)

6) Which equation matches amplitude 5, period π, midline y = -2, and a maximum at x = 0?

Y = 5cos(2x) - 2

Y = 5cos(x/2) - 2

Y = 5cos(2x) + 2

Y = -5cos(2x) - 2

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

Right π/3

None

Left π/6

Right π/6

8) The vertical asymptotes of y = csc(x + π/6) occur at

X = π/6 + 2kπ

X = π/2 + kπ

X = -π/6 + kπ

X = kπ

9) What is the range of y = -3 csc(x) + 2?

Y ≤ -5 or y ≥ 1

Y ≤ -1 or y ≥ 5

(-∞, -1) ∪ (1, ∞)

Y ≥ 5

10) What is the range of y = 6 cos(x) - 1?

[-6, 6]

[-5, 7]

(-∞, -1] ∪ [1, ∞)

[-7, 5]

11) What is the period of y = sin((5/2)x- π)?

4π/5

5π/2

2π/5

π/5

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

Y = 2

Y = -2

Y = -5

Y = 5

13) What is the midline of y = -7 sin(x) + 9?

Y = -7

Y = 9

Y = 0

Y = 7

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

2/5

5/3

1/3

3/5

15) What is the amplitude of y = -4.2 cos(x + 1)?

1

0

4.2

-4.2

16) What is the period of y = csc(x/9)?

18π

9π/2

2π/9

9π

17) What is the period of y = sec(πx)?

π

2

2π

1

18) What is the period of y = cot(x/7)?

π/7

π

2π

7π

19) What is the period of y = tan(√3 x)?

π/3

π

π/√3

3π

20) What is the period of y = cos(0.75x)?

3π/8

2π/3

4π/3

8π/3

Applied/Descriptive Questions