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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