SOLUTION: I was helping a friend with her trig homework and we both got stuck on this one problem. It has to do with solving a trigonometric equation. We know we have to use an identity, but

Question 364398: I was helping a friend with her trig homework and we both got stuck on this one problem. It has to do with solving a trigonometric equation. We know we have to use an identity, but we just haven't found the right one to make it easy. Here is the problem:
Solve for x, where x is greater than or equal to zero, but less than or equal to 2 pi.

sin(x) + (square root of 3)cos(x)= -1
I tried several identities and tried to find a double or half angle formula that might help, but I just haven't been able to get one to work...everytime I replace something with an identity, I make it larger and more complex, I'm not simplifying anything.
Answer by nyc_function(2741) (Show Source): You can put this solution on YOUR website!
sin(x) + (square root of 3)cos(x) = -1

Add 1 to both sides.

sin(x) + (square root of 3)cos(x) + 1 = 0

Did you try the quadratic formula?

Let a = 1, b = sqrt[3] and c = 1

Using the quadratic formula I got:

x = (-sqrt[3] + i)/2

AND

x = (-sqrt[3] - i)/2

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