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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