Use the power reducing formula to rewrite the expression calculator

Precalculus

Mason P.

asked • 03/25/21

Use power reducing formulas to rewrite: 12sin^4 x

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Raymond B. answered • 03/25/21

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12sin^4(x) = 9/2 -6cos(2x) + (3/2)cos(4x)

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Use the power reducing formula to rewrite the expression calculator

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+0  

 Power Reducing Formula

+1

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Use the power reducing formula to rewrite the expression calculator
+322 

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

0 users composing answers..

    2+0 Answers

     #1

    Use the power reducing formula to rewrite the expression calculator
    +6236 

    +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

    Use the power reducing formula to rewrite the expression calculator
    +322 

    +1

    I actually just figured it out.  Thank you though

    Ruublrr  Dec 1, 2018


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