Question

Can you explaing me how:

tan^-1(2/2)=pi/4

How became tan^-1(2/2) in pi/4.

originary exercise complex number

z^9=2+2j

Answer 1

can u tell what is the orignal question

Answer 2

Ok one momente a make a photo.

Answer 3

\[\tan^{-1}(\dfrac{2}{2})\\=\tan^{-1}(1)=45^{\circ}=\dfrac{\pi}{4}\]

Answer 4

ok and how 45 grade in pi/4?

Answer 5

its on the unit circle

Answer 6

w

Answer 7

suppose this is right angled triangle

and here it is also iscoceles triangle

so the two sides opposite to \(45^{\circ}\)

are equal

now we know that

\(\tan \theta =\dfrac{opposite~ side}{adjacent~side}\)

so

\(\tan 45^{\circ} =\dfrac{a}{a}\)

\(\tan 45^{\circ} =1\\\)

hence

\(45^{\circ}=\tan ^{-1} 1\)

Answer 8

and \(45^{\circ}\) in radian is \((\dfrac{\pi}{4})\)

Answer 9

can I make it without calculator?

Answer 10

or onliy wiht calclator?

Answer 11

which thing ?

Answer 12

a sorry radians

Answer 13

well the idea is that \(\pi\) radian is equal to \(180^{\circ}\)

to \(~~~~~\dfrac{\pi}{4}\\
=\dfrac{180}{4}\\
=\dfrac{90}{2}\\
=45^{\circ}\)

Answer 14

or conversly

\(\pi\) radian is equal to \(180^{\circ}\)

\(~~~~~45^{\circ}\\
=45\times \dfrac{\pi}{180}\\
=\dfrac{\pi}{4}\\
\)

Answer 15

ok only one thing about it

Answer 16

than I divide 45pi/180 by 45 ?

Answer 17

a ok I understand.

also Pi must be alone without number?

Answer 18

\(\pi\) is not alone it has some value like \(3.14..\)

but we usually write angles in it in the degrees \(\Huge \theta ^{\circ}\) symbol \(\huge \pi\)

Answer 19

yes ok that is so

Answer 20

but I mean the number before pi

Answer 21

by every exercise liek this I must divide from Pi. the pi must stay alone wihtout other numbers?

Answer 22

for example if u have to to write \(360^{\circ}\)

in radian then it can be written as

\(\Large 360^{\circ}\\
\Large =360\times \dfrac{\pi}{180}\\
\Large =2\pi\\\)

Answer 23

a ok I understand thank you very much what arguments I must study for this exerscise? I understand all but I will study it for sin and cos

Answer 24

here is a good link for u
http://www.mathsisfun.com/geometry/unit-circle.html

Answer 25

at first trignometry is difficult,but once u practice , it will be as easy as \(1+1=2\)

Answer 26

Ok will do but first I must study relevant things for test. thanky you

Answer 27

welcome