Let Px y denote the point where the terminal side of an angl

Let P(x, y) denote the point where the terminal side of an angle theta meets the unit circle. If P is in Quadrant IV and x = 3/4, find: (a) cot(theta) (b) csc(theta).

Solution

In 4th quadrant , x = 3/4 , circle is of unit radius

So , Hypotenuse= 1 , x = Base = 3/4 , Perpendicular = - (1² - (3/4)²)^1/2 = -( 7/16)^1/2 = - 7/4 ( - due to negative y)

(a) cot = Base /Perpendicular = (3/4) / (-7/4) = - 3/7

(b) csc = Hypotenuse/Perpendicular = 1/(-7/4) = - 4/7