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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