Find the Exact Value tan(-315 degrees )

Problem

tan(−315^∘)

Solution

1. Find a coterminal angle by adding 360^∘ to the given negative angle to find its equivalent position within the first rotation.

θ=−315^∘+360^∘=45^∘

2. Identify the reference angle and the quadrant. Since 45^∘ is in the first quadrant, the reference angle is 45^∘ and all trigonometric functions are positive.

tan(−315^∘)=tan(45^∘)

3. Evaluate the tangent using the known values for special angles, where tan(45^∘)=1

tan(45^∘)=1

Final Answer

tan(−315^∘)=1

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