Simplify sin(330)

Problem

sin(330)

Solution

1. Identify the angle's position on the unit circle. The angle 330 is in the fourth quadrant because it is between 270 and 360

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

θ′=360−330=30

3. Determine the sign of the sine function. In the fourth quadrant, the ycoordinates are negative, so sin(330) must be negative.

sin(330)=−sin(30)

4. Evaluate the sine of the reference angle using known trigonometric values.

sin(30)=1/2

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

sin(330)=−1/2

Final Answer

sin(330)=−1/2

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