Question 776345: I need to solve for x in 10sin^2(x) – 9cos(x) – 12 = 0
I've tried pythagorean identities 10 (1-cos^2(x)) – 9cos(x) – 12 = 0 but don't know where to go from there. I know it needs to be in a form that can be used for the zero product rule (no addition or subtraction in the expression), and then from there I need to use the unit circle (which I can do).
I also tried power reducing/double angle, but that was very confusing for me.
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! 10sin^2(x) - 9cos(x) - 12 = 0
To get an expression involving only terms in cos(x), we use the identity sin^2(x)+cos^2(x) = 1 -> sin^2(x) = 1 - cos^2(x)
10(1-cos^2(x)) - 9cos(x) - 12 = 0
10cos^2(x) + 9cos(x) + 2 = 0
This can be solved using the quadratic formula, using cos(x) as the variable.
Alternatively, the expression can actually be factored this way:
(10cos(x)+5)(cos(x)+2/5) = 0
This gives 10cos(x) = -5 or cos(x) = -1/2
and cos(x) = -2/5
I'll leave it as an exercise to solve for x from here
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