Find the Exact Value sin(240)

Problem

sin(240^∘)

Solution

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

2. Determine the sign of the sine function in Quadrant III. In this quadrant, the sine of an angle is negative.

3. Calculate the reference angle θ^′ For an angle in Quadrant III, the reference angle is found using the formula θ^′=θ−180^∘

θ^′=240^∘−180^∘

θ^′=60^∘

4. Apply the reference angle property. The value of sin(240^∘) is equal to −sin(60^∘)

sin(240^∘)=−sin(60^∘)

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

sin(240^∘)=−√(,3)/2

Final Answer

sin(240^∘)=−√(,3)/2

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