What is $-sin^4theta$ in terms of non-exponential trigonometric functions?

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What is $-sin^4theta$ in terms of non-exponential trigonometric functions?

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Answer 1 · 2016-03-18T13:59:26

$= -3/8 - (cos 4t)/8 + (cos 2t)/2$

Explanation:

$2sin^2 t = (1 - cos 2t)$ .
Square the 2 sides:
$4sin^4 t = (1 - cos 2t)^2 = 1 + cos^2 2t - 2cos 2t$
Replace $cos^2 2t$ by $(1 + cos 4t)/2$
$4sin^4t = 1 + 1/2 + cos (4t)/2 - 2cos 2t =$
$3/2 + (cos (4t)/2) - 2cos 2t$
Divide both sides by -4 -->

$- sin^4 t = - 3/8 - (cos 4t)/8 + (cos 2t)/2$

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What is $-sin^4theta$ in terms of non-exponential trigonometric functions?

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