Question

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

7 tan3x - 21 tan x = 0

Answer 1

its \(\tan 3x\)
or \(\tan^3x\)
??

Answer 2

tan^3 sorry

Answer 3

okk,
factor out 7tan x from left side
what u get ?

Answer 4

That mainly my confusion, I missed a day and I don't know how to factor out 7tan x. How do I factor?

Answer 5

factoring 'x' from \(x^3\) gives \(x (x^2)\)
right ?

Answer 6

so, factoring tan x from \(\tan^3x\) will give you \(\tan x (\tan^2x)\)

so your left side becomes

\(\Large 7 \tan x (\tan^2 x-3) = 0 \)

see if you get this step properly...

Answer 7

oh okay I got that. How do I find the solutions after factoring

Answer 8

when ab = 0
a= 0 or b = 0

so we get
\( \tan x = 0\) or \(\tan^2x = 3\)

can you find for which angles are the above equations true ?

Answer 9

\[\tan ^{2} x=3\] ?

Answer 10

tan x = 0 for which angles in 0 to 2pi ??

tan^2 x = 3
so,
\( \tan x= \sqrt3\) for which angles in 0 to 2pi ??

or
\( \tan x= -\sqrt3\) for which angles in 0 to 2pi ??

Answer 11

tan x= -\[\sqrt{3}\]

Answer 12

for what values of x??

Answer 13

am i finding out x?

Answer 14

yes...

Answer 15

Okay. idk how to find x

Answer 16

do you have unit circle ?

Answer 17

yes

Answer 18

good,
for tan x to be -sqrt 3

sin x = -sqrt 3/2
cos x = 1/2
for which angle ?

or

sin x = sqrt 3/2
cos x = -1/2
for which angle ?

Answer 19

I'm not understanding this

Answer 20

didn't you attempt easier problems before going to this one?
like sin x =0 or cos x = 1/2
something like that ?
if not, this is a difficult problem to start with...

Answer 21

No he just gave me this one and told me to solve it...

Answer 22

Can you show me the steps in finding the answer?

Answer 23

can you use calculator ?

Answer 24

Yes I can

Answer 25

cool, so can't you just plug in tan x = -sqrt 3 in you calculator and it gives you x values ??

Answer 26

Its shoes me its graph of tan x =-3^2