Explain why arctan(1) = 45° or π/4.

Explanation below

Step-by-step explanation:

Inverse Trigonometric Functions

They are defined as the inverse of the basic trigonometric functions which are sine, cosine, tangent, cotangent, secant, and cosecant.

The corresponding inverse functions are called arcsin, arccos, arctan, arccot, arcsec, arccsc.

These inverse functions in trigonometry are used to get the angle with any of the trigonometry ratios.

For example,

Then:

Since:

Or, equivalently:

Then:

Or:

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)