Find the Exact Value cos(330)

Problem

cos(330^∘)

Solution

1. Identify the reference angle by finding the difference between 330^∘ and 360^∘

(θ_ref)=360^∘−330^∘

(θ_ref)=30^∘

2. Determine the quadrant in which 330^∘ lies. Since 270^∘<330^∘<360^∘ the angle is in Quadrant IV.

3. Determine the sign of the cosine function in Quadrant IV. In this quadrant, the xcoordinates are positive, so cos(330^∘) is positive.

cos(330^∘)=cos(30^∘)

4. Evaluate the exact value of cos(30^∘) using the unit circle or a special right triangle.

cos(30^∘)=√(,3)/2

Final Answer

cos(330^∘)=√(,3)/2

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