Find the Reference Angle tan(405)

Problem

tan(405^∘)

Solution

1. Identify the given angle, which is 405^∘

2. Find the coterminal angle within the range of 0^∘ to 360^∘ by subtracting 360^∘ from the original angle.

405^∘−360^∘=45^∘

3. Determine the quadrant of the coterminal angle. Since 45^∘ is between 0^∘ and 90^∘ it lies in Quadrant I.

4. Apply the reference angle rule for Quadrant I. For an angle θ in Quadrant I, the reference angle θ^′ is equal to the angle itself.

θ^′=45^∘

Final Answer

Reference Angle of *405^∘=45^∘

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