Find the Exact Value sin(600)

Problem

sin(600^∘)

Solution

1. Find the coterminal angle by subtracting 360^∘ from 600^∘ to bring the angle within the standard 0^∘ to 360^∘ range.

600^∘−360^∘=240^∘

2. Determine the quadrant of the angle 240^∘ Since 180^∘<240^∘<270^∘ the angle lies in Quadrant III.

3. Calculate the reference angle for an angle in Quadrant III by subtracting 180^∘ from the angle.

(θ_ref)=240^∘−180^∘=60^∘

4. Determine the sign of the sine function in Quadrant III. Since the ycoordinate is negative in Quadrant III, sin(240^∘) is negative.

sin(240^∘)=−sin(60^∘)

5. Substitute the known value for sin(60^∘) which is √(,3)/2

sin(240^∘)=−√(,3)/2

Final Answer

sin(600^∘)=−√(,3)/2

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