Find the Exact Value cos(-210)

Problem

cos(−210^∘)

Solution

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

cos(−210^∘)=cos(210^∘)

2. Find the reference angle for 210^∘ Since 210^∘ is in the third quadrant, subtract 180^∘ from the angle.

Reference Angle=210^∘−180^∘=30^∘

3. Determine the sign of the cosine function in the third quadrant. In the third quadrant, cosine values are negative.

cos(210^∘)=−cos(30^∘)

4. Substitute the known value for cos(30^∘) which is √(,3)/2

cos(210^∘)=−√(,3)/2

Final Answer

cos(−210^∘)=−√(,3)/2

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