Simplify sin(210)

Problem

sin(210)

Solution

1. Identify the angle's position on the unit circle. The angle 210 is in the third quadrant because it is between 180 and 270

2. Determine the reference angle. For an angle in the third quadrant, the reference angle is found by subtracting 180 from the angle.

(θ_ref)=210−180=30

3. Determine the sign of the sine function. In the third quadrant, the ycoordinates are negative, so sin(210) must be negative.

sin(210)=−sin(30)

4. Evaluate using the known value for the sine of 30

sin(30)=1/2

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

sin(210)=−1/2

Final Answer

sin(210)=−1/2

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