Find the Exact Value tan(510)

Problem

tan(510)

Solution

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

510−360=150

2. Identify the quadrant for 150 which lies in Quadrant II where the tangent function is negative.

90<150<180

3. Determine the reference angle by subtracting the angle from 180

180−150=30

4. Apply the tangent value for the reference angle and attach the appropriate sign for Quadrant II.

tan(150)=−tan(30)

5. Substitute the known value for tan(30) which is 1/√(,3) or √(,3)/3

tan(30)=√(,3)/3

Final Answer

tan(510)=−√(,3)/3

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