Question

Could somebody explain to me why the following statement is true, " arctan(1) = pi/4"

Answer 1

Do you know what arctan is?

Answer 2

What is pi/4? It is 90 degrees. Now check if \(\tan 90^{\circ} = 1\)

Answer 3

Yes, I understand that it is the inverse of the tangent function.

Answer 4

Is \(\tan90^{\circ} = 1\)?

Answer 5

ParthKohli can put it much more simply than I can T.T

Answer 6

haha

Answer 7

Isn't tan at 90 undefined?

Answer 8

In other words, \(\tan = \large {\sin \over \cos}\)

Answer 9

Yes it is undefined then ^_^

Answer 10

pi/4 is 45 degrees o.o

Answer 11

** tan 45, he means.

Answer 12

OMG SORRY

Answer 13

\( \color{Black}{\Rightarrow \tan45^{\circ} = 1}\)

Answer 14

This is awkward...

Answer 15

I guess you already know the important ratios, do you?

Answer 16

Don't you guys think we're complicating things a bit?

Answer 17

Haha no.

\(\sin 90 = 1\)

\( \color{Black}{\Rightarrow\cos 0 = 1 }\)

\( \color{Black}{\Rightarrow \tan 45 = 1 }\)

Answer 18

\[\arctan\left(\frac{\text {opposite}}{\text{adjacent}}\right) = \theta\]
\[\arctan\left(\frac 11\right) =45°= \pi/4\]

Answer 19

The biggest issue is that I am completely knew to trig and like when I learned algebra, I needed steps to find my solutions. Could somebody give me some step-by-step instructions to solving the problem?

Answer 20

\( \color{Black}{\Rightarrow \tan 45 = \large {\sin 45 \over \cos 45 } = {\Large {1 \over \sqrt2} \over {1 \over \sqrt2}} }\)

Answer 21

Well, you know the relationship between functions and their inverses?

Answer 22

That leads us to the statement tan 45 = 1

Answer 23

Yes, I understand that (for lack of a better explanation) the domain and range is flipped.

Answer 24

Well you can refer to @UnkleRhaukus 's diagram

Answer 25

(90,1) becomes (1,90) where 90 = x and f(x) is sin.

Answer 26

Similarly, (45,1) becomes (1,45)
that's it ^_^

Answer 27

other than that, for instance,
Let f be a bijective* function, such that g = f^-1
then if a is in the range of f, then
what's f(g(a)) ?

Answer 28

if your arc tan is one it means the opposite and adjacent sides are equal. the sum of the angles in a triangle is 180°
the triangle has a right angle , because we are using trig ratios , and the angles are equal because the opp and adjacent are equal
180°-90°=2x45°

Answer 29

\[\tan45 = 1\]

Or,\[\tan(\pi /4) = 1\]
Because,
\[45 = \pi /4\]

So,

\[\tan^{-1} (1) = \tan^{-1} (\tan \pi /4) = \pi /4\] is the answer...

Answer 30

Long story, short, if you compose a function with its inverse, they'd cancel each other out :)
so since
tan (pi/4) = 1

then

arctan[tan (pi/4)] = arctan 1
since arctan is the inverse of tan, they'd cancel out so...
pi/4 = arctan 1