Find the Value Using the Unit Circle sin(150 degrees )

Problem

sin(150^∘)

Solution

1. Identify the angle 150^∘ on the unit circle.

2. Determine the reference angle by subtracting 150^∘ from 180^∘

180^∘−150^∘=30^∘

3. Locate the quadrant for 150^∘ which is Quadrant II.

4. Recall that the sine function corresponds to the ycoordinate on the unit circle and is positive in Quadrant II.

5. Evaluate the sine of the reference angle 30^∘

sin(30^∘)=1/2

6. Apply the sign for Quadrant II to the result.

sin(150^∘)=1/2

Final Answer

sin(150^∘)=1/2

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