Circular functions

Question

if tanθ = -4/3 and sinθ < 0, find the value of cscθ.

Answer 1

Since the tan is negative and the sin is negative, this angle must be in the 4th quadrant. With a tangent of -4/3, the opposite side is -4 and the adjacent side is 3. The find the csc, we need to find the hypotenuse. You can use the Pythagorean theorem. However this is a special triangle that is common. So I know the hypotenuse is 5. csc = hypotenuse/opposite = -5/4