Simplify sin(300)

Problem

sin(300)

Solution

1. Identify the angle's position on the unit circle. The angle 300 is in the fourth quadrant because 270<300<360

2. Determine the reference angle. For an angle θ in the fourth quadrant, the reference angle θ′ is calculated as 360−θ

θ′=360−300=60

3. Apply the sign rule for the sine function. In the fourth quadrant, the sine of an angle is negative.

sin(300)=−sin(60)

4. Substitute the known value for the sine of the reference angle.

sin(60)=√(,3)/2

5. Combine the sign and the value to find the final result.

sin(300)=−√(,3)/2

Final Answer

sin(300)=−√(,3)/2

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