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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