Quadratic trig equations

Question

Find all angles, 0° ≤ θ < 360° , that satisfy the equation below, to the nearest 10th of a degree. If there is no solution, write no solution.

tan²θ−2tanθ−3=0

Answer 1

let x=tanT

then

x^2 -2x -3=0

factor

(x-3)(x+1) =0

set each factor=0

x+1=0, x-3=0

x=-1 or 3

tanT= -1 or 3

T = the angle whose tangent = -1 or 3

use a calculator with an inverse tangent function

T=-45 +180n degrees where n= any integer

or

71.6 + 180n degrees where n = any integer

but you only want angles from 0 to 360 degrees

so

Theta= 71.6, 135, 251.6, or 315 degrees