Find the Exact Value cos(280)

Problem

cos(280^∘)

Solution

1. Identify the angle's quadrant. Since 270^∘<280^∘<360^∘ the angle 280^∘ is in the fourth quadrant.

2. Determine the reference angle. In the fourth quadrant, the reference angle (θ_r*e*ƒ) is calculated by subtracting the angle from 360^∘

(θ_r*e*ƒ)=360^∘−280^∘

(θ_r*e*ƒ)=80^∘

3. Apply the sign rule for the cosine function. In the fourth quadrant, the cosine of an angle is positive.

cos(280^∘)=cos(80^∘)

4. Evaluate the exactness. The angle 80^∘ is not a standard unit circle angle (like 30^∘ 45^∘ or 60^∘. Therefore, the exact value is expressed in terms of the cosine of the reference angle or its cofunction.

cos(80^∘)=sin(90^∘−80^∘)

cos(80^∘)=sin(10^∘)

Final Answer

cos(280^∘)=cos(80^∘)

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