Find the Exact Value sin(120)

Problem

sin(120)

Solution

1. Identify the reference angle by finding the distance from the angle to the nearest 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 ycoordinate is positive, so sin(120) is positive.

3. Apply the trigonometric identity for reference angles: sin(θ)=sin(180−θ) for angles in the second quadrant.

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

Final Answer

sin(120)=√(,3)/2

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