Find the Value Using the Unit Circle sin(150)

Problem

sin(150)

Solution

1. Identify the position of 150 on the unit circle. Since 90<150<180 the angle lies in the second quadrant.

2. Determine the reference angle by subtracting the angle from 180

(θ_ref)=180−150=30

3. Recall the sine value for the reference angle 30 from the unit circle or special right triangles.

sin(30)=1/2

4. Determine the sign of the sine function in the second quadrant. In the second quadrant, ycoordinates are positive, so sin(θ) is positive.

sin(150)=sin(30)

Final Answer

sin(150)=1/2

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