Find the Exact Value sin(210 degrees )

Problem

sin(210)

Solution

1. Identify the quadrant of the angle. Since 180<210<270 the angle 210 lies in Quadrant III.

2. Determine the sign of the sine function. In Quadrant III, the sine of an angle is negative.

3. Calculate the reference angle. The reference angle θ′ for an angle in Quadrant III is found using θ′=θ−180

θ′=210−180=30

4. Evaluate the sine of the reference angle. The exact value of sin(30) is 1/2

5. Apply the sign from step 2 to the value from step 4.

sin(210)=−sin(30)=−1/2

Final Answer

sin(210)=−1/2

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