Find the Exact Value cos(120 degrees )

Problem

cos(120)

Solution

1. Identify the reference angle by finding the distance from the terminal side of 120 to the x-axis.

(θ_ref)=180−120=60

2. Determine the quadrant in which 120 lies. Since 90<120<180 the angle is in Quadrant II.

3. Determine the sign of the cosine function in Quadrant II. In this quadrant, the x-coordinates are negative, so cos(θ) is negative.

cos(120)=−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(120)=−1/2

Final Answer

cos(120)=−1/2

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