Question

Let θ be an angle in quadrant IV such that cosθ = 4/9.
Find the exact values of csc θ and cot θ.

I am just completely lost! Thanks!

Answer 1

4 along x axis
9 along hypotenuse sloping down
so y = - sqrt(81 -16) = -sqrt(65)
so sin T = -sqrt(65) /9

so csc T = 1/sin T = -9/sqrt 65

cot T = cos T/sin T = (4/9 ) / -(sqrt 65)/9
= 4/sqrt 65 = (4 sqrt 65) / 65