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

Jun 1, 2016

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.

${3}^{2} + {b}^{2} = {5}^{2}$
$9 + {b}^{2} = 25$
${b}^{2} = 16$
$b = 4$

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