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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