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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