Find the Exact Value sin(200)

Problem

sin(200)

Solution

1. Identify the angle and its quadrant. The angle 200 is in the third quadrant because 180<200<270

2. Determine the reference angle. For an angle θ in the third quadrant, the reference angle θ′ is calculated as θ−180

3. Calculate the reference angle value.

θ′=200−180=20

4. Apply the sign rule for the sine function. In the third quadrant, the sine of an angle is negative.

sin(200)=−sin(20)

5. Conclude that since 20 is not a standard unit circle angle, the exact value is expressed in terms of the sine of the reference angle.

Final Answer

sin(200)=−sin(20)

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