Find the Exact Value cos(240 degrees )

Problem

cos(240)

Solution

1. Identify the quadrant of the angle. Since 180<240<270 the angle 240 lies in Quadrant III.

2. Determine the reference angle. In Quadrant III, the reference angle (θ_ref) is calculated as θ−180

(θ_ref)=240−180=60

3. Determine the sign of the cosine function. In Quadrant III, the cosine of an angle is negative.

cos(240)=−cos(60)

4. Evaluate the cosine of the reference angle using the unit circle or special right triangles.

cos(60)=1/2

5. Combine the sign and the value to find the final result.

cos(240)=−1/2

Final Answer

cos(240)=−1/2

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