Simplify cos(240)

Problem

cos(240)

Solution

1. Identify the reference angle by finding the distance from the angle to the nearest x-axis. Since 240 is in the third quadrant, subtract 180 from the angle.

240−180=60

2. Determine the sign of the cosine function in the third quadrant. In the third quadrant, the x-coordinates are negative, so the cosine value is negative.

cos(240)=−cos(60)

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

cos(60)=1/2

4. 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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