Trigonometry pre calc 12

Question

Angle 0 lies in quadrant IV and tan 0 = -4/5.  Find the exact values of the other two trigonometric ratios.

Answer 1

tangent is opposite side/adjacent side = -4/5, hypotenuse = sqr(25+16) = sqr41

sine is opposite/hypotenuse = -4/sqr41

cos(theta) = 5/sqr41

other trig functions are

cot(theta) = -5/4

sec(theta) = sqr41/5= the inverse of the cosine

csc(theta) = -sqr41/4 = inverse of the sine