Find the Exact Value sin(140)

Problem

sin(140^∘)

Solution

1. Identify the angle and its quadrant. The angle 140^∘ is in the second quadrant because 90^∘<140^∘<180^∘

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

3. Calculate the reference angle value.

θ^′=180^∘−140^∘=40^∘

4. Apply the sine property for the second quadrant. In the second quadrant, the sine function is positive, so sin(θ)=sin(180^∘−θ)

sin(140^∘)=sin(40^∘)

5. Conclude the exact value. Since 40^∘ is not a standard unit circle angle (like 30^∘ 45^∘ or 60^∘, the exact value is expressed in terms of the sine function.

Final Answer

sin(140^∘)=sin(40^∘)

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