Evaluate the integral.
{eq}\int_{0}^{2 \pi} \sin^2( \frac{1}{3} \theta) \, \mathrm{d}\theta {/eq}
Question:
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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View this answerHere, 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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Chapter 23 / Lesson 1Learn to define basic trigonometric identities. Discover the double-angle, half-angle, and other identities. Learn how to use trigonometric identities. See examples.