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Chapter 4: Problem 13

Find the point \((x, y)\) on the unit circle that corresponds to the real number \(t\). $$ t=\frac{5 \pi}{6} $$

Short Answer

Expert verified
The point \((- \frac{1}{2}, \frac{\sqrt{3}}{2})\) on the unit circle corresponds to the real number \(t =\frac{5 \pi}{6}\).

Step by step solution

01

Understand the Unit Circle

In a unit circle, the 'x' coordinate is the cosine of the angle in radians and the 'y' coordinate is the sine of the angle in radians. As the problem provides an angle \(t = \frac{5 \pi}{6}\), use this to find the coordinates (\(x,y\)).
02

Find x-coordinate

Calculate the cosine of the given angle, \(t\), to find the x-coordinate. So, \(x = \cos(t) = \cos(\frac{5 \pi}{6})\).
03

Find y-coordinate

Calculate the sine of the angle \(t\) to find the y-coordinate. So, \(y = \sin(t) = \sin(\frac{5 \pi}{6})\).
04

Establish final points

The final points \((x, y)\) correspond to the real number \(t\) on the unit circle are \((- \frac{1}{2}, \frac{\sqrt{3}}{2})\).

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