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Chapter 9: Q. 6 (page 582)

$\cos \frac{2 π}{3} =________.$

Short Answer

Expert verified

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

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 $\cos \frac{2 π}{3}$ as $\cos (π - \frac{π}{3}) .$

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

Thus,

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

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Most popular questions from this chapter

Findzwand $\frac{z}{w}$ . Leave the answers in polar form.

role="math" localid="1646661399572" $z = 2 + 2 i w = \sqrt{3} - i$

In Problems 61–66, graph each pair of polar equations on the same polar grid. Find the polar coordinates of the point(s) of intersection and label the point(s) on the graph.

$r = 3; r = 2 + 2 \cos θ$

In Problems 39-54,the poplar coordinates of a point are given.Find rectangular coordinates of each point.

$(- 2, 0)$

$\tan^{- 1} (- 1) =_______$

In Problems 13–28, transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation. Verify your graph using a graphing utility.

$θ = \frac{π}{3}$

See all solutions

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