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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