# Precalculus : Set Up an Equation That Models Harmonic Motion

## Example Questions

### Example Question #1 : Harmonic Motion

Create an equation modelling temperature , with highest temperature at , which is  degrees and lowest temperature of  degrees which occurs at .  Assume that this model is sinusoidal and use a cosine model.

Possible Answers:

Correct answer:

Explanation:

This can be written in the general form of:

Since the maximum occurs at , we can arbitrarily choose  since cosine would be maximum when the inner term is equal to

To determine , let's determine the period first.

The period is equal to twice the length between adjacent crest and trough.

For us that is:

To determine , we do

To determine

To determine ,

The entire regression can therefore be written as:

The only thing that can be changed to keep the regression the same is the phase shift , and sign of the amplitude . The other two terms must be kept as they are.

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