Question

Solve the equation for the interval [0,2π]: 2sin^2(x) = sin(x)

          Solve the equation for the interval [0,2π]: 2sin^2(x) = sin(x)
        

Added by Shawn A.

Precalculus with Limits
Precalculus with Limits
Ron Larson 2nd Edition
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Solve the equation for the interval [0,2π]: 2sin^2(x) = sin(x)
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Transcript

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00:01 One thing to consider in this problem is the double angle formula for cosine of 2x, and sign of x is fine.
00:10 Now, the tricky thing then is there are three different formulas for cosine of 2x.
00:16 So i always tell my students to pick the one that deals with the other trig function in the problem.
00:21 Well, the other trig function is sign.
00:23 So just rewrite, you know, if you're looking at your formula sheet or if you haven't memorized, it's 1 minus 2 sine squared of x, and everything else is still the same.
00:38 I think the way i would do this problem is just a me thing is i would add 2 sine squared to the right side, add sine of x to the right side, and subtract 1 to the right side.
00:51 Because now you can factor this...
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