Question

How do you solve `5sin^2x-8sinx=3` in the interval [0,360]?

Answer 1

`90^@; 216^@87; 323^@13`

Explanation:

`f(x) = 5sin^2 x - 8sin x - 3 = 0`
Solve the above quadratic equation for sin x.
Since a + b + c = 0, the shortcut gives:
sin x = 1 and `sin x = c/a = - 3/5`
a. sin x = 1 --> `x = pi/2 = 90^@`
b. `sin = -3/5`
Calculator and unit circle give 2 solutions:
`x = - 36^@87`, or `x = 360 - 36.87 = 323^@13` (co-terminal), and:
`x = 180 - (- 36.87) = 216^@87`