Simplify sin(240)

Problem

sin(240)

Solution

1. Identify the reference angle by finding the distance from the angle to the nearest part of the xaxis. Since 240 is in the third quadrant, subtract 180 from the angle.

(θ_ref)=240−180=60

2. Determine the sign of the sine function in the third quadrant. In the third quadrant, the ycoordinates are negative, so the sine value is negative.

sin(240)=−sin(60)

3. Evaluate the sine of the reference angle using the unit circle or special right triangles.

sin(60)=√(,3)/2

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

sin(240)=−√(,3)/2

Final Answer

sin(240)=−√(,3)/2

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