Question

Based on the set of points in the graph, determine the equation that
would match the graph.
(1 point)
f (θ) = 1.5 cos( θ)
π
3
f (θ) = 1.5 sin(3θ)
f (θ) = 1.5 cos(3θ)
f (θ) = 1.5 sin( θ)

Answer 1

To determine which function matches the graph based on the description of the set of points, we can analyze the options provided. Here are some attributes of the functions that might help:

1. **Amplification**: All functions have an amplitude of 1.5, meaning they will oscillate between -1.5 and +1.5.

2. **Cosine and Sine Functions**:
- \( \cos(θ) \) and \( \sin(θ) \) oscillate once as θ goes from 0 to \( 2π \).
- \( \cos(3θ) \) and \( \sin(3θ) \) oscillate three times as θ goes from 0 to \( 2π \) (they will have a period of \( \frac{2π}{3} \)).

3. **Frequency**:
- If the graph has more oscillations within a given interval, then functions with the factor of 3 inside the cosine or sine (like \( \sin(3θ) \) or \( \cos(3θ) \)) will be the right candidates.

Based on the characteristics described above, if the graph shows more oscillations (three complete cycles within \( 0 \) to \( 2π \)), then the equation should include the factor of three in the argument of cosine or sine.

However, if it only shows one complete oscillation, then the cosine or sine function without the multiple would fit.

Let me know if you have more specific information about the graph or its behavior, so I can help you choose the correct equation!