Precalculus Mason P. Use power reducing formulas to rewrite: 12sin^4 x Follow • 1 Add comment More Report
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Raymond B. answered • 03/25/21 Tutor 5 (2) Math, microeconomics or criminal justice About this tutor › About this tutor › 12sin^4(x) = 9/2 -6cos(2x) + (3/2)cos(4x) Upvote • 1 Downvote
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+0
Power Reducing Formula
+1
1056
2
Use the power-reducing formulas as many times as possible to rewrite the expression in terms of the first power of the cosine.
7 cos4 x
Ruublrr Dec 1, 2018
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2+0 Answers
#1
+1
\(\text{I assume you mean }7\cos^4(x)\)
\(\cos^4(x) =\left( \cos^2(x)\right)^2 = \\ \left(\dfrac{\cos(2x)+1}{2}\right)^2 = \\ \dfrac 1 4 + \dfrac 1 2 \cos(2x) + \dfrac 1 4 \cos^2(2x)\\ \text{repeat the process on the term on the right}\\ \dfrac 1 4 \cos^2(2x) = \dfrac 1 8 (1 + \cos(4x)) \\ \text{so combining everything}\\ 7\cos^4(x) = \dfrac{7}{8} (4 \cos (2 x)+\cos (4 x)+3)\)
.Rom Dec 1, 2018
#2
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I actually just figured it out. Thank you though
Ruublrr Dec 1, 2018
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