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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