Find the Exact Value cos(-300 degrees )

Problem

cos(−300^∘)

Solution

1. Apply the even-odd identity for the cosine function, which states cos(−θ)=cos(θ)

cos(−300^∘)=cos(300^∘)

2. Find the coterminal angle or use the unit circle to identify the position of 300^∘ Since 300^∘ is in the fourth quadrant, the cosine value will be positive.

300^∘=360^∘−60^∘

3. Determine the reference angle by subtracting the angle from 360^∘

Reference Angle=360^∘−300^∘=60^∘

4. Evaluate the cosine of the reference angle using the special right triangle values.

cos(60^∘)=1/2

5. Combine the results noting that cosine is positive in the fourth quadrant.

cos(300^∘)=1/2

Final Answer

cos(−300^∘)=1/2

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