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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