Find the Exact Value cos(300)

Problem

cos(300^∘)

Solution

1. Identify the reference angle by finding the difference between 300^∘ and the nearest x-axis value, which is 360^∘

(θ_ref)=360^∘−300^∘

(θ_ref)=60^∘

2. Determine the quadrant in which 300^∘ lies. Since 270^∘<300^∘<360^∘ the angle is in Quadrant IV.

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

cos(300^∘)=cos(60^∘)

4. Evaluate the exact value of cos(60^∘) using the unit circle or special right triangles.

cos(60^∘)=1/2

Final Answer

cos(300^∘)=1/2

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