Find the Value Using the Unit Circle sin(120)

Problem

sin(120^∘)

Solution

1. Identify the angle 120^∘ on the unit circle. This angle is located in the second quadrant.

2. Determine the reference angle by subtracting 120^∘ from 180^∘

180^∘−120^∘=60^∘

3. Recall the sine value for the reference angle 60^∘

sin(60^∘)=√(,3)/2

4. Determine the sign of the sine function in the second quadrant. Since the ycoordinate is positive in the second quadrant, the sine value remains positive.

sin(120^∘)=sin(60^∘)

Final Answer

sin(120^∘)=√(,3)/2

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