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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