Question

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

Answer 1

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