Q6. What is the equation for the sinusoid pictured at right?

Background

Topic: Sinusoidal Functions (Graphing Trigonometric Functions)

This question tests your ability to interpret the graph of a cosine or sine function and match it to its algebraic equation. You need to identify amplitude, period, phase shift, and vertical shift from the graph.

Key Terms and Formulas:

• Amplitude: The maximum distance from the midline to the peak/trough.

• Period: The length of one complete cycle.

• Phase Shift: Horizontal shift of the graph.

• Vertical Shift: How much the graph is moved up or down.

• General form: or

Step-by-Step Guidance

1. Examine the graph to determine the amplitude. The amplitude is the distance from the midline to the maximum or minimum value.

2. Find the period by measuring the distance along the x-axis for one complete cycle of the wave.

3. Identify the midline (the horizontal line halfway between the maximum and minimum values) to determine the vertical shift.

4. Check where the graph starts relative to the midline to determine if it is a sine or cosine function and if there is a phase shift.

5. Compare these characteristics to the given answer choices to match the equation to the graph.

Try solving on your own before revealing the answer!