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Expert-verified Found in: Page 582 ### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465 # $\mathrm{cos}\frac{2\mathrm{\pi }}{3}=________.$

The value of $\mathrm{cos}\frac{2\mathrm{\pi }}{3}=-\frac{1}{2}.$

See the step by step solution

## Step 1. Given Information

The cosine function is a periodic function. The ratio of the adjacent side to the hypotenuse of the right-angled triangle is called the cosine function.

## Step 2. Filling the blank

We can write $\mathrm{cos}\frac{2\mathrm{\pi }}{3}$ as $\mathrm{cos}\left(\mathrm{\pi }-\frac{\mathrm{\pi }}{3}\right).$

As we know cosine function is negative in the second quadrant.

Thus,

$\mathrm{cos}\frac{2\mathrm{\pi }}{3}=\mathrm{cos}\left(\mathrm{\pi }-\frac{\mathrm{\pi }}{3}\right)\phantom{\rule{0ex}{0ex}}\mathrm{cos}\frac{2\mathrm{\pi }}{3}=-\mathrm{cos}\left(\frac{\mathrm{\pi }}{3}\right)\phantom{\rule{0ex}{0ex}}\mathrm{cos}\frac{2\mathrm{\pi }}{3}=-\frac{1}{2}$ ### Want to see more solutions like these? 