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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