Pre Calc Homework - Solve problems involving the inverses of trigonometric functions

Question

The line y= 3/5 x passes through the origin in the x,y plane.  What is the measure of the angle that the line makes with the positive x-axis?  Give your answer in degrees and radians.

Answer 1

Per the rise-over-run concept for the slope, we can construct a right triangle with lengths 3 and 5 as the legs. Then, we can use the legs to find the angle as follows:

tanθ = 3/5

θ = tan^-1(3/5)

θ is approximately 30.96 degrees or 0.54 radians.