Simplify sin(150)

Problem

sin(150)

Solution

1. Identify the angle in the unit circle. The angle 150 is located in the second quadrant.

2. Determine the reference angle. The reference angle for an angle θ in the second quadrant is 180−θ

3. Calculate the reference angle value.

180−150=30

4. Determine the sign of the sine function. In the second quadrant, the sine of an angle is positive.

5. Apply the trigonometric identity for the reference angle.

sin(150)=sin(30)

6. Evaluate the sine of the reference angle using known values.

sin(30)=1/2

Final Answer

sin(150)=1/2

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