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.
https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&ved=0ahUKEwiaify36ofNAhXDqh4KHdBhBpYQjRwIBw&url=http%3A%2F%2Fwww.mathinary.com%2Ftriangle_right.jsp&psig=AFQjCNG63ECTT47j-kKr-SCTHHHZkW5vXQ&ust=1464904973628283

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.

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&ved=0ahUKEwiaify36ofNAhXDqh4KHdBhBpYQjRwIBw&url=http%3A%2F%2Fwww.mathinary.com%2Ftriangle_right.jsp&psig=AFQjCNG63ECTT47j-kKr-SCTHHHZkW5vXQ&ust=1464904973628283

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