# How do you find sin theta if cos theta = 3/5?

##### 1 Answer

Jun 1, 2016

#### Answer:

You can sketch a right triangle and write out the side lengths, to then use the Pythagorean theorem to find sin θ.

#### Explanation:

First, draw a right triangle.

Then, fill in the values you know. A cosine function is equivalent to the **adjacent side divided by the hypotenuse** , from **SOH-CAH-TOA.**

So, our **adjacent side can be 3** , and **the hypotenuse can be 5.**

Then, we can use the Pythagorean theorem **( #a^2 + b^2 = c^2#)** to find the missing side length.

We found our three sides: **4, 5, and 9.**

We know from SOH-CAH-TOA that the sine function is equivalent to the opposite side length divided by the hypotenuse length. So:

**sin θ = 4/9**