Given that cos0= 7/12 and the angle 0 is in the fourth quadrant, find the value for sin 0

Answer 1

The basic trig identity is that sin^2 + cos^2 = 1. You can use that equation to determine the sine value. In the fourth quadrant the sine value is negative.

Answer 2

If you set up a coordinate plane and draw in your right triangle in the 4th quadrant with θ as the reference angle, and keeping in mind that sine will always be negative in the 4th quadrant, you can label the adjacent side ( which runs along the x -axis) as 7 and the hypotenuse will be 12. By Pythagorean Theorem, the other leg of the triangle ( the one running vertical down from the x-axis) will be √95. So the sine ratio will end up being √95/12.

** Note: this is simply an alternative method from using the identity to determine the value of the ratio. Either method is good and will produce the same value for the sine ratio.