Find the Exact Value cos(-210 degrees )

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^∘ by determining its distance from the 180^∘ horizontal axis.

Reference Angle=210^∘−180^∘=30^∘

3. Determine the quadrant of the angle 210^∘ Since 180^∘<210^∘<270^∘ the angle lies in Quadrant III.

4. Determine the sign of the cosine function in Quadrant III. In this quadrant, the cosine value is negative.

cos(210^∘)=−cos(30^∘)

5. 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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