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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