Pre-Calculus Question?

Question

Assume theta lies in quadrant 3 and the terminal side theta is perpendicular to the line y= -4x.
Part 1. Determine sin (theta).
Part 2. Determine sec (theta).

Answer 1

If terminal side perpendicular to y = -4x, equation is y = x/4, and rise/run = 1/4 = tan Θ. hypotenuse of reference triangle must be √17, so sin Θ = -1/√17, cos Θ = -4/√17, and so sec Θ = -√17 / 4.