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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