Chapter 6: Q 117. (page 382)

Find two negative and three positive angles, expressed in radians, for which the point on the unit circle that corresponds to each angle is $(\frac{1}{2}, \frac{\sqrt{3}}{2})$ .

Short Answer

Expert verified

The angles are $\sin t = \frac{\sqrt{3}}{2}, c s c t = \frac{2}{\sqrt{3}}, \cos t = \frac{1}{2}, \tan t = \sqrt{3}$

Step by step solution

Step 1. Given information .

Consider the given point $(\frac{1}{2}, \frac{\sqrt{3}}{2})$ .

Step 2. Finding negative and positive angles.

We follow the definition of six trigonometric function using $P (\frac{1}{2}, \frac{\sqrt{3}}{2}) = (x, y)$ where $x = \frac{1}{2}, y = \frac{\sqrt{3}}{2}$ .

Since the points are positive so there are positive angles.

$\sin t = y = \frac{\sqrt{3}}{2}, c s c t = \frac{1}{y} = \frac{2}{\sqrt{3}}, \cos t = x = \frac{1}{2} \tan t = \frac{y}{x} = \sqrt{3},$

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Find two negative and three positive angles, expressed in radians, for which the point on the unit circle that corresponds to each angle is $(\frac{1}{2}, \frac{\sqrt{3}}{2})$ .

Short Answer

Step by step solution

Step 1. Given information .

Step 2. Finding negative and positive angles.

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Find two negative and three positive angles, expressed in radians, for which the point on the unit circle that corresponds to each angle is 12,32.

Short Answer

Step by step solution

Step 1. Given information .

Step 2. Finding negative and positive angles.

One App. One Place for Learning.

Most popular questions from this chapter

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Find two negative and three positive angles, expressed in radians, for which the point on the unit circle that corresponds to each angle is $(\frac{1}{2}, \frac{\sqrt{3}}{2})$ .