Find the Exact Value cos(-510)

Problem

cos(−510)

Solution

1. Find the coterminal angle by adding 360 repeatedly until the angle is within the standard range of 0 to 360

θ=−510+360=−150

θ=−150+360=210

2. Identify the quadrant for 210 Since 180<210<270 the angle lies in Quadrant III.

3. Determine the reference angle θ′ for an angle in Quadrant III using the formula θ′=θ−180

θ′=210−180=30

4. Apply the sign rule for cosine in Quadrant III. In this quadrant, the cosine function 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(−510)=−√(,3)/2

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