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Chapter 4: Problem 62

In Exercises \(61-86,\) use reference angles to find the exact value of each expression. Do not use a calculator. $$\sin 300^{\circ}$$

Short Answer

Expert verified
The exact value of \(\sin(300^{\circ})\) is \(-\sqrt{3}/2\).

Step by step solution

01

Identify the quadrant

Firstly, determine which quadrant the angle falls in. A full circle is 360 degrees. Therefore, since 300 degrees is less than 360 but more than 270, it falls into the fourth quadrant.
02

Identify the reference angle

The reference angle can be found by subtracting the given angle from 360 if it's in the fourth quadrant. So, the reference angle is \(360^{\circ} - 300^{\circ} = 60^{\circ}\).
03

Determine the sign

In the fourth quadrant, the sine function is negative. This is because on a unit circle, the y-values (which represent sin values) are negative in the fourth quadrant.
04

Compute the value

The sine value of the reference angle is \(\sin(60^{\circ}) = \sqrt{3}/2\). Apply the negative sign as determined in step 3 to get the final answer.

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