# The Sine Wave

The Sine Wave

This is a representation of various lingo language that is currently available. For those parents who are looking for Multiplication Worksheets you can check out the Scholastic.com site where they have material for K-8 grades. For those going through AP math the examples below might be helpful.

As described in Sine & Cosine Definitions, **t** is the** length of an arc** on the unit circle. If the sine function is graphed with **t** on the **horizontal axis** and **sin(t)** on the **vertical axis**, this is the resulting curve:

Important points:

- The curve
**oscillates**between**1**and**-1**. - The curve
**repeats every 2pi**.

A look at the unit circle shows the reasons. As **t **proceeds around the unit circle, sin(t) goes up to 1 then down to -1, and then repeats as **t** keeps going around the circle. It repeats every **2pi** because the **circumference** of the unit circle is**2pi**.

Cosine

The graph of cosine is the same as sine, but shifted by -pi/2.

So **sin(t) = cos(t – pi/2)**. For oscillation, either can be used to the same effect. A very interesting relation between sine and cosine is that the **slope** of the sine curve at any value of **t** is **cos(t)**.

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