# Vertical Translation, Amplitude, Period, Phase Shift, and Range of Cosine and Sine Functions | Summary and Q&A

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May 22, 2018
by
The Math Sorcerer
Vertical Translation, Amplitude, Period, Phase Shift, and Range of Cosine and Sine Functions

## TL;DR

This video explains the concepts of phase shift, amplitude, period, and vertical translations in trigonometric functions using examples and formulas.

## Key Insights

• π The equation format for trigonometric functions is y = c + a sin(bx - d) or y = c + a cos(bx - d).
• π¦ The vertical translation is denoted by the value of c in the equation.
• β The amplitude is the absolute value of the coefficient a in the equation.
• ποΈ The period of a trigonometric function is given by 2Ο divided by the coefficient of x, denoted by b.
• βΊοΈ The phase shift can be found by reversing the sign of the value inside the parentheses after x, denoted by d.
• π Rewriting equations in the proper form helps identify and calculate the various aspects of trigonometric functions.
• π§‘ The range of a trigonometric function can be expanded or contracted based on the amplitude.

## Transcript

in this video we're going to put everything together we're going to talk about phase shifts amplitude period and also vertical translations so we have say y equals c plus a sign parenthesis b x minus d parenthesis so when we have something that looks like this or something that looks like this so I'm going to write the same thing except with the co... Read More

### Q: What are the four aspects discussed in the video regarding trigonometric functions?

The four aspects discussed in the video are vertical translations, amplitude, period, and phase shift.

### Q: How do you find the period of a trigonometric function?

The period of a trigonometric function can be found by taking 2Ο divided by the coefficient of x in the equation.

### Q: How can you identify the phase shift in a trigonometric function?

The phase shift can be identified by looking at the value inside the parentheses after x, and reversing its sign.

### Q: How do you determine the amplitude of a trigonometric function?

The amplitude of a trigonometric function is the absolute value of the coefficient in front of the trigonometric term.

## Summary & Key Takeaways

• The video discusses the equation format for trigonometric functions and how to identify vertical translations, amplitude, period, and phase shift.

• An example is used to demonstrate how to rewrite an equation in the correct format and find all the mentioned aspects.

• The video also briefly mentions finding the range of the function and how it is affected by the amplitude.