Let (-2,3) be a point on the terminal side of θ. Find the exact values of Cosθ, Cscθ, and Tanθ.

Answer 1

This places the angle x in the 2nd quadrant, where cosine is negative, sine is positive.

We can form a right triangle in the 2nd quadrant with leg length 2 (horizontally) and length length 3 (vertically), so that the hypotenuse = SQRT(13).

The cosine x = -2/SQRT(13)

The sine x = 3/SQRT(13)

The cosecant x = 1/sine = SQRT(13)/3

The tangent x = -3/2