2sin squaredx-5sinx=3 the interval 0 degrees<x<360 degrees?

Answer 1

Rewriting:

2(sinx)^2 - 5sinx = 3
2(sinx)^2 - 5sinx - 3 = 0
(2sinx +1)(sinx - 3) = 0

2sinx +1 = 0
2sinx = -1
sinx = -0.5
x = 270

sinx - 3 = 0
sinx = 3
No solutions for this one, since sinx has to be between -1 and 1.

Answer 2

Just treat this problem as a regular quadratic making it 2x^2 - 5x-3 = 0 "
Factor it out and then plug in sinx. Then take out any answers that don't fit into the interval.