Evaluate the integral.

{eq}\int_{0}^{2 \pi} \sin^2( \frac{1}{3} \theta) \, \mathrm{d}\theta {/eq}


Evaluate the integral.

{eq}\int_{0}^{2 \pi} \sin^2( \frac{1}{3} \theta) \, \mathrm{d}\theta {/eq}

Half-Angle Identities:

Half-angle identities are trigonometric identities that can be used to express a trigonometric function of a half-angle as a trigonometric function of a single angle. One of the half-angle identities is {eq}\displaystyle \sin\left(\frac{\theta}{2}\right) = \pm \sqrt{\frac{1-\cos(\theta)}{2}} {/eq}, which gives us:

{eq}\sin^2(\theta) = \displaystyle \frac{1-\cos(2\theta)}{2} {/eq}

Answer and Explanation: 1

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Here, we'll simply implement the trigonometric identity {eq}\sin^2(\theta) = \displaystyle \frac{1-\cos(2\theta)}{2} {/eq}.

This will give us the...

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Trigonometric Identities: Definition & Uses


Chapter 23 / Lesson 1

Learn to define basic trigonometric identities. Discover the double-angle, half-angle, and other identities. Learn how to use trigonometric identities. See examples.

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