Find the Exact Value sin(240 degrees )

Problem

sin(240)

Solution

1. Identify the reference angle by finding the distance from the angle to the nearest x-axis. Since 240 is in the third quadrant, subtract 180 from the angle.

240−180=60

2. Determine the sign of the sine function in the third quadrant. In the third quadrant, the y-coordinates 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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