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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