Caitlyn C.

# Why do sine waves cycle between 1 and -1?

In the sine function y=sin(x), why does the sinusoid travel between 1 and -1

## 2 Answers By Expert Tutors

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Tutor
4.9 (27)

Math/Physics Tutor

MICHAEL E.

tutor
Hello Andy,
I like your answer, because it is very simple to follow. However, I like to add a little more to it. Consider the coordinate grid, with the origin at (0,0). In the 1st and 2nd quadrants, the opposite side is always a positive y-coordinate and the hypotenuse is always positive. Therefore Opposite/hypotenuse will be positive and between 0 and 1. In the 3rd and 4th quadrants, the opposite side will be always be a negative y-coordinate, and since the hypotenuse is always positive, Opposite/hypotenuse will be negative and between -1 and 0. Thank you for sharing.
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05/26/18

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