Find the Value Using the Unit Circle sin(240)

Problem

sin(240^∘)

Solution

1. Identify the position of 240^∘ on the unit circle. Since 180^∘<240^∘<270^∘ the angle lies in the third quadrant.

2. Calculate the reference angle by subtracting 180^∘ from the given angle.

240^∘−180^∘=60^∘

3. Determine the sine value of the reference angle using known unit circle values.

sin(60^∘)=√(,3)/2

4. Apply the correct sign for the third quadrant. In the third quadrant, the ycoordinate (sine) is negative.

sin(240^∘)=−sin(60^∘)

5. Substitute the value to find the final result.

sin(240^∘)=−√(,3)/2

Final Answer

sin(240^∘)=−√(,3)/2

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