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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 9: Q. 6 (page 582)

$\cos \frac{2 蟺}{3} =________.$

Short Answer

Expert verified

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

Step by step solution

01

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.

02

Step 2. Filling the blank

We can write $\cos \frac{2 蟺}{3}$ as $\cos (蟺 - \frac{蟺}{3}) .$

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

Thus,

$\cos \frac{2 蟺}{3} = \cos (蟺 - \frac{蟺}{3}) \cos \frac{2 蟺}{3} = - \cos (\frac{蟺}{3}) \cos \frac{2 蟺}{3} = - \frac{1}{2}$

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