Find the Exact Value sin(120 degrees )

Problem

sin(120^∘)

Solution

1. Identify the reference angle by finding the distance from the terminal side to the xaxis. Since 120^∘ is in the second quadrant, the reference angle is 180^∘−120^∘=60^∘

2. Determine the sign of the sine function in the second quadrant. In the second quadrant, the ycoordinates are positive, so sin(120^∘) is positive.

3. Apply the known exact value for the sine of the reference angle. The value of sin(60^∘) is √(,3)/2

4. Combine the sign and the value to find the final result.

Final Answer

sin(120^∘)=√(,3)/2

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