Question

How do you find the general solutions for `5cos(x) + 4= Sec(x)`?

Answer 1

Solve: 5cos X + 4 = sec x

Explanation:

`5cos x + 4 = 1/cos x`
`5cos^2 x + 4cos x - 1 = 0.`
Since a - b + c = 0, use the shortcut. The 2 real roots are:
cos x = - 1, and `cos x = -c/a = 1/5`

a. cos x = -1 --> `x = pi + kpi`

b. cos x = 1/5 = 0.20 --> `x = +- 78.46 deg + 2k(360)`