Question

How do you find the solution for `tan^2 A - 3tanA - 4 = 0` for [-90,0]?

Answer 1

Solve tan^2 A - 3tan A - 4 = 0 for (-90, 0)

Ans: `(7pi)/4` or `315^@`

Explanation:

Call tan A = t, we get a quadratic equation:
t^2 - 3t - 4 = 0.
Since (a - b + c = 0), use Shortcut. The 2 real roots are t = -1 and
t = -c/a = 4.
The trig unit circle and Trig Table of Special Arcs give:

a. t = tan A = -1 --> `A = (3pi)/4` and `A = (3pi)/4 + pi = (7pi)/4`
b. t = tan A = 4 --> A = 75.96 and A = 75.96 + 180 = `255^@96`

Inside the interval (-90, 0) there is only one answer: `(7pi)/4`
or `315^@`