Find the Exact Value cos(140)

Problem

cos(140)

Solution

1. Identify the angle and the desired trigonometric function, which is cos(140)

2. Determine the quadrant of the angle. Since 90<140<180 the angle lies in the second quadrant.

3. Apply the reference angle formula for the second quadrant, which is (θ_ref)=180−θ

4. Calculate the reference angle: 180−140=40

5. Determine the sign of the cosine function in the second quadrant. In the second quadrant, cosine is negative.

6. Relate the original expression to its reference angle: cos(140)=−cos(40)

7. Conclude that since 40 is not a standard unit circle angle (30,45,60, the exact value is expressed in terms of the cosine of the reference angle.

Final Answer

cos(140)=−cos(40)

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