Find the Exact Value cos(510)

Problem

cos(510^∘)

Solution

1. Find the coterminal angle by subtracting 360^∘ from the given angle to bring it within the standard 0^∘ to 360^∘ range.

510^∘−360^∘=150^∘

2. Determine the quadrant of the angle 150^∘ Since 90^∘<150^∘<180^∘ the angle lies in Quadrant II.

3. Find the reference angle for an angle in Quadrant II by subtracting the angle from 180^∘

180^∘−150^∘=30^∘

4. Determine the sign of the cosine function in Quadrant II. In Quadrant II, cosine values are negative.

cos(150^∘)=−cos(30^∘)

5. Substitute the known value for cos(30^∘) which is √(,3)/2

−cos(30^∘)=−√(,3)/2

Final Answer

cos(510^∘)=−√(,3)/2

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