Sine and Cosine Graphs Worksheet

Sine and Cosine Graphs

Read each question carefully and provide accurate answers. Show all your work for full credit.

1. What is the amplitude of the function y = 3sin(2x - π) + 1?

2. Which of the following represents the period of the function y = cos(x/3) - 2?

3. The   of a sinusoidal function is half the distance between its maximum and minimum values.

4. A horizontal shift of a trigonometric graph is also known as a  .

5. Describe how the graph of y = -2sin(x + π/4) would be transformed from the parent function y = sin(x).

6. The range of the function y = 4cos(x) is [-4, 4].

7. A vertical shift of 3 units up for a sine graph changes its amplitude.

8. Graph one full period of the function y = 2cos(x - π/2). Label the amplitude, period, and phase shift.

Amplitude:  

Period:  

Phase Shift:  

9. The depth of water at a certain dock varies with the tides. The depth varies from a minimum of 4 feet to a maximum of 10 feet. A full tidal cycle takes 12 hours. Write a sinusoidal function to model the depth of the water D (in feet) as a function of time t (in hours), assuming that at t=0, the depth is at its average.