Problem 62
Question
In Exercises \(61-86,\) use reference angles to find the exact value of each expression. Do not use a calculator. $$\sin 300^{\circ}$$
Step-by-Step Solution
Verified Answer
The exact value of \(\sin(300^{\circ})\) is \(-\sqrt{3}/2\).
1Step 1: 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.
2Step 2: 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 \(360^{\circ} - 300^{\circ} = 60^{\circ}\).
3Step 3: 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.
4Step 4: 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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Problem 62
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