# Solving Trigonometric Equations with multiple solutions

1. Dec 1, 2012

1. The problem statement, all variables and given/known data
Solve each equation for solutions on the interval 0 ≤ x ≤ 2∏.
Code (Text):

2 sin x = √3

3. The attempt at a solution
Okay so I was able to solve this one:

• 2 sin x = √3
• sin x = (√3) / 2

So i got x = ∏/3 ; 2∏/3 ; 4∏/3 ; 5∏/3

I substituted the x's into the original problem, and ∏/3 and 2∏/3 give +(√3). The other two give -(√3). Are the one's that give negative results also solutions? If so, is this only true for (±√x), or is the sign always a significant factor?

2. Dec 1, 2012

### HallsofIvy

Staff Emeritus
No, if $sin(x)= -\sqrt{3}/2$ then $2sin(x)= -\sqrt{3}$ which is NOT the original equation. Those values of x do NOT satisfy the equation and are NOT solutions. In particular, $\sqrt{a}$ is NOT the same as either $-\sqrt{a}$ or $\pm\sqrt{a}$.

3. Dec 1, 2012

Thank you for clarifying (: