Need help! Would greatly appreciate it.

Question

If cos (theta) = 4/19 and theta is i quadrant IV, find sin (theta)

Answer 1

In the 4th quadrant, cos(theta) is positive 4/19.  In this case, 4/19 represents the ratio of the adjacent side of theta divided by the hypotenuse.  Using the Pythagorean Theorem,  a^2+b^2 = c^2 we can find the opposite side of theta.  

4^2 + b^2 = 19^2

          b^2 = 19^2 - 4^2

          b^2 = 345

              b = sqrt(345)

 

Sin (theta) = opposite / hypotenuse

                = sqrt(345)/ 19

                = .9776

 

But remember the sin (theta) is actually negative in the 4th quadrant.  So Sin (theta) = -.9776

 

Have a great day.

 

Pythagorean Theorem