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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