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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