Evaluate tan(405 degrees )

Problem

tan(405^∘)

Solution

1. Identify the angle as being greater than 360^∘ which means it has completed more than one full revolution around the unit circle.

2. Find the coterminal angle by subtracting 360^∘ from the given angle to find a value within the standard 0^∘ to 360^∘ range.

405^∘−360^∘=45^∘

3. Apply the periodic property of the tangent function, which states that tan(θ+360^∘⋅n)=tan(θ)

tan(405^∘)=tan(45^∘)

4. Evaluate the tangent of the resulting reference angle using known trigonometric values.

tan(45^∘)=1

Final Answer

tan(405^∘)=1

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