Find all solutions in the interval [0, 2π).

7 tan2x - 21 tan x = 0

Question

Find all solutions in the interval [0, 2π). 

7 tan2x - 21 tan x = 0

zasharra · Answer

@mathmate

zasharra · Answer

@tkhunny

irishboy123 · Answer

i'd say always rip it into sin and cos

i reckon you have: $7 \tan2x - 21 \tan x = 0$

zasharra · Answer

I have the numbers but i need it in fraction form

zasharra · Answer

^2

zasharra · Answer

7 tan ^2x - 21 tan x=0

tkhunny · Answer

Treat it like a quadratic equation.  Factor and solve.

tkhunny · Answer

No sine and cosine silliness.  You should know where tan(x) = 0 and tan(x) = 3.

irishboy123 · Answer

Mmmmm

$7 \dfrac{\sin 2x}{\cos 2x}  - 21 \dfrac{\sin x}{\cos x} = 0$

$ \dfrac{\sin 2x}{\cos 2x}  - 3 \dfrac{\sin x}{\cos x} = 0$

$ \dfrac{2 \sin x \cos x}{\cos 2x}  - 3 \dfrac{\sin x}{\cos x} = 0$

nil solution is $\sin x = 0$.......

$ \dfrac{2  \cos x}{\cos 2x}  - 3 \dfrac{1}{\cos x} = 0$

$ \dfrac{2  \cos^2 x}{1}  - 3 \dfrac{\cos 2x}{1} = 0$


Hang on a mo, its:

$7 \tan^2(x) - 21 \tan( x) = 0$

And not 

$7 \tan(2x) - 21 \tan (x) = 0$

Grrrr