find sin(theta)

Question

given cos(theta)=3/5 in quadrant IV, find sin(theta)

Answer 1

If cos(theta) = 3/5, you can create a right triangle with the adjacent leg begin 3 and the hypotenuse being 5.  Find the other leg using Pythagorean theorem.  You should come out with 4.  Now, Sin(theta) will be opposite over hypotenuse.  This will be 4/5, but we are in the 4th quadrant, where all of sine is negative.  

 

So, final answer sin(theta) = -4/5