Find the Exact Value cos(240)

Problem

cos(240)

Solution

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

2. Determine the sign of the cosine function in Quadrant III. In this quadrant, the xcoordinates are negative, so cos(240) must be negative.

3. Calculate the reference angle (θ_r*e*ƒ) by subtracting 180 from the given angle.

(θ_r*e*ƒ)=240−180=60

4. Apply the reference angle rule for cosine.

cos(240)=−cos(60)

5. Substitute the known exact value for cos(60) which is 1/2

cos(240)=−1/2

Final Answer

cos(240)=−1/2

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