How do you find sin theta if cos theta = 3/5?
You can sketch a right triangle and write out the side lengths, to then use the Pythagorean theorem to find sin θ.
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 (
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