How do you express ${sin}^{4} θ - {sin}^{3} θ + {cos}^{2} θ$ $sin^4theta - sin^3theta + cos^2theta$ in terms of non-exponential trigonometric functions?

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How do you express ${sin}^{4} θ - {sin}^{3} θ + {cos}^{2} θ$ $sin^4theta - sin^3theta + cos^2theta$ in terms of non-exponential trigonometric functions?

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Answer 1 · 2016-07-02T03:26:05

Transform trig expression.

Explanation:

Apply the 2 trig identities:
${cos}^{2} t = \frac{1 + cos 2 t}{2}$ $cos ^2 t = (1 + cos 2t)/2$
${sin}^{2} t = \frac{1 - cos 2 t}{2}$ $sin^2 t = (1 - cos 2t)/2$
${sin}^{4} t - {sin}^{3} t + {cos}^{2} t = {sin}^{2} t (sin t) (sin t - 1) + {cos}^{2} t =$ $sin^4 t - sin^3 t + cos^2 t = sin^2 t(sin t)(sin t - 1) + cos ^2 t =$
$= (\frac{1 - cos 2 t}{2}) (sin t - 1) sin t + \frac{1 + cos 2 t}{2}$ $= ((1 - cos 2t)/2) (sin t - 1)sin t + (1 + cos 2t)/2$

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How do you express ${sin}^{4} θ - {sin}^{3} θ + {cos}^{2} θ$ $sin^4theta - sin^3theta + cos^2theta$ in terms of non-exponential trigonometric functions?

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How do you express ${sin}^{4} θ - {sin}^{3} θ + {cos}^{2} θ$ $sin^4theta - sin^3theta + cos^2theta$ in terms of non-exponential trigonometric functions?