Trigonometry : Phase Shifts

Study concepts, example questions & explanations for Trigonometry

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Example Questions

Example Question #1 : Phase Shifts

Identify the phase shift of the following equation.

Possible Answers:

Correct answer:


If we use the standard form of a sine function

the phase shift can be calculated by .  Therefore, in our case, our phase shift is

Example Question #2 : Trigonometric Graphs

Which of the following is equivalent to 

Possible Answers:

Correct answer:


The first zero can be found by plugging 3π/2 for x, and noting that it is a double period function, the zeros are every π/2, count three back and there is a zero at zero, going down.

A more succinct form for this answer is  but that was not one of the options, so a shifted cosine must be the answer.

The first positive peak is at π/4 at -1, so the cosine function will be shifted π/4 to the right and multiplied by -1. The period and amplitude still 2, so the answer becomes .

To check, plug in π/4 for x and it will come out to -2.

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