Solving trignometric equation

Hi, the problem is:

solve on the interval 0 ≤ x ≤ 2pi

2 sin^2 x - 3 sin x -2 = 0

I factored the equation to (2x + 1)(x - 2)

then separated to 2x + 1 = 0 and x - 2 = 0

finally sin x = -1/2 and sin x = 2

I figured out one of the x's equals 210 degrees or 7pi/6. Sin x = 2 does not seem like a solution. The given choices each have more than one possible solution, and I have only found one. How do I find the other ones?

Re: Solving trignometric equation

review your unit circle ...

$\displaystyle \sin{x} = -\frac{1}{2}$ at $\displaystyle x=\frac{7\pi}{6}$ and $\displaystyle x=\frac{11\pi}{6}$

Re: Solving trignometric equation

You are right to discard Sin x = 2. But there are two solutions for Sin x = -1/2.

Re: Solving trignometric equation

Quote:

Originally Posted by

**Frederick** Hi, the problem is:

solve on the interval 0 ≤ x ≤ 2pi

2 sin^2 x - 3 sin x -2 = 0

I factored the equation to (2x + 1)(x - 2)

then separated to 2x + 1 = 0 and x - 2 = 0

A technical point- since x appears in the orginal equation, it is not a good idea to use "x" to represent "sin(x)". Use some other letter.

Quote:

finally sin x = -1/2 and sin x = 2

I figured out one of the x's equals 210 degrees or 7pi/6. Sin x = 2 does not seem like a solution. The given choices each have more than one possible solution, and I have only found one. How do I find the other ones?