Find the Exact Value tan(495)

Problem

tan(495^∘)

Solution

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

495^∘−360^∘=135^∘

2. Identify the quadrant for the angle 135^∘ Since 90^∘<135^∘<180^∘ the angle lies in Quadrant II.

3. Determine the reference angle for 135^∘ in Quadrant II by subtracting the angle from 180^∘

180^∘−135^∘=45^∘

4. Apply the tangent sign for Quadrant II. In Quadrant II, the tangent function is negative.

tan(135^∘)=−tan(45^∘)

5. Substitute the known value for tan(45^∘) which is 1

−tan(45^∘)=−1

Final Answer

tan(495^∘)=−1

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