Find the Exact Value sin(150)

Problem

sin(150^∘)

Solution

1. Identify the reference angle by finding the distance from the angle to the nearest x-axis. Since 150^∘ is in the second quadrant, the reference angle is 180^∘−150^∘=30^∘

2. Determine the sign of the sine function in the second quadrant. In the second quadrant, the y-coordinates are positive, so sin(150^∘) is positive.

3. Apply the reference angle property sin(θ)=sin(180^∘−θ) for angles in the second quadrant.

4. Evaluate the sine of the reference angle using the unit circle or special right triangles, where sin(30^∘)=1/2

Final Answer

sin(150^∘)=1/2

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