Find the Exact Value tan(315 degrees )

Problem

tan(315)

Solution

1. Identify the reference angle by finding the difference between 315 and the nearest x-axis value, which is 360

(θ_ref)=360−315=45

2. Determine the quadrant in which 315 lies. Since 270<315<360 the angle is in Quadrant IV.

3. Apply the sign rule for the tangent function. In Quadrant IV, the tangent of an angle is negative.

tan(315)=−tan(45)

4. Evaluate the tangent of the reference angle using known trigonometric values.

tan(45)=1

5. Combine the sign and the value to find the final result.

tan(315)=−1

Final Answer

tan(315)=−1

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