Find the Exact Value tan(405)

Problem

tan(405^∘)

Solution

1. Identify the angle and determine its coterminal equivalent within the standard 0^∘ to 360^∘ range by subtracting 360^∘

θ=405^∘−360^∘

2. Simplify the angle to find the primary rotation.

θ=45^∘

3. Apply the property that trigonometric functions of coterminal angles are equal.

tan(405^∘)=tan(45^∘)

4. Evaluate the tangent of the reference angle using the unit circle or special right triangles, where tan(45^∘)=sin(45^∘)/cos(45^∘)=√(,2)/2/√(,2)/2

tan(45^∘)=1

Final Answer

tan(405^∘)=1

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