Question

Find all solutions to the equation. 7 sin2x - 14 sin x + 2 = -5

Answer 1

I'm assuming that's a sin²(x), and not a sin(2x), right?


First, collect the terms.

7sin²(x) - 14sin(x) + 7 = 0


Factorise the quadratic.

Due to the high numbers, I'm going to use the quadratic formula to factorise the quadratic.

(-b ± √(b² - 4ac)) / 2a

Therefore

sin(x) = 1
(for both negative and positive of the quadratic formula)


Refer to the quadrant diagram.

sin(x) is a positive, meaning our answer will be on the first and second quadrant.


x = arcsin(1) = 90°


Since you don't provide an interval in your question, I'm going to assume that the interval is 0° ≤ θ ≤ 360°.


Referring again to the quadrant diagram, the solutions are going to be:

θ = 90°, 180°