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Question

Let , (−2,3) be a point on the terminal side of θ. Find the exact values of sinθ, cscθ, and cotθ.

Answer 1

(-2,3) is in the 2nd quadrant where sines, cosecant are >0, cotangents <0

3 is the opposite side, -2 is the adjancent side,

use the Pythagorean Theorem to fin

the hypotenuse = square root of (3^2 +2^2) = sqr13

sin(theta) = opposite side/hypotenuse = 3/sqr13

csc(theta) =1/sin(theta) = hypotenuse/opposite side = (sqr13)/3

cot(theta) = adjacent side/opposite side = -2/3