How does one find the maximum value of $$ 5\sin(x)+4\sin(2x) $$ without using calculus?
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2Wait, Kim Jong Un is on math.stackexchange? Where's Dennis Rodman? – Stephen Sep 10 '14 at 17:27
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Note that $\sin ( 2x ) = 2 \sin ( x ) \cos (x )$ – PenasRaul Sep 10 '14 at 17:28
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Put $t=\sin x$ and make an equation only in terms of $t$ using trigonometric identities. You might use:
$$\sin 2x=2\sin x\cos x\\\sin^2x+\cos^2x=1\implies \cos x=\pm\sqrt{1-\sin^2x}$$
to get:
$$Z=5t\pm8t\sqrt{1-t^2}$$
This might be solved without calculus, but if possible, I'll add that.
RE60K
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You should consider actually that $\cos (x ) = \pm \sqrt{ 1- \sin^2 (x ) }$ – PenasRaul Sep 10 '14 at 17:30
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You should probably consider showing OP how to proceed from $5t\pm 8t\sqrt{1-t^2}$ without using calculus? – Kim Jong Un Sep 10 '14 at 17:35
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i guess calculus is required now to find the max value of from here on.I want to solve this without the use of calculus. – TSP1993 Sep 10 '14 at 17:37