Find the Exact Value sin(660)

Problem

sin(660)

Solution

1. Find the coterminal angle by subtracting 360 from the given angle until it is within the range of 0 to 360

660−360=300

2. Determine the quadrant where the angle 300 terminates. Since 270<300<360 the angle is in Quadrant IV.

3. Calculate the reference angle for an angle in Quadrant IV by subtracting the angle from 360

(θ_ref)=360−300=60

4. Determine the sign of the sine function in Quadrant IV. In Quadrant IV, the sine value is negative.

sin(660)=−sin(60)

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

sin(60)=√(,3)/2

6. Apply the sign to find the final exact value.

sin(660)=−√(,3)/2

Final Answer

sin(660)=−√(,3)/2

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