Evalute arctan(1) and arctan(0)

[aaaa202]

I want to evalute arctan(1) and arctan(0). Of course I could plug into my calculator but this is an analysis course and I think they want me to do as much proper mathetmatics as possible. Therefore: Is there any way to see what the values might be, like you can see what the value of sin(∏/2) for instance.

 

[MednataMiza]

What do you see when you look at this plot ?

Or you can simply take the table of values of the Tan function and analyse them.

 

[I like Serena]

I want to evalute arctan(1) and arctan(0). Of course I could plug into my calculator but this is an analysis course and I think they want me to do as much proper mathetmatics as possible. Therefore: Is there any way to see what the values might be, like you can see what the value of sin(∏/2) for instance.

Hi aaaa202!

Suppose we pick a right triangle with sides x and y.
Then the tangent of the angle is (y/x).

arctan(1) is the angle for which (y/x)=1.
For instance the triangle with sides 1, 1, and $\sqrt 2$.
Can you tell how large this angle is?