Find the Exact Value tan(-315)

Problem

tan(−315)

Solution

1. Use the odd-even property of the tangent function, which states that tan(−θ)=−tan(θ)

tan(−315)=−tan(315)

2. Find a coterminal angle for 315 within the first rotation, or recognize its position in the fourth quadrant.

315=360−45

3. Determine the reference angle by subtracting the angle from 360 since it lies in Quadrant IV.

(θ_ref)=360−315=45

4. Apply the quadrant sign for tangent. In Quadrant IV, tangent is negative.

tan(315)=−tan(45)

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

tan(315)=−1

6. Combine the results from the first step to find the final value.

tan(−315)=−(−1)=1

Final Answer

tan(−315)=1

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