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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