Question

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

7 tan^3x - 21 tan x = 0

Answer 1

factor 7tan x out

Answer 2

ok so i get tan^2x -3

Answer 3

do i set both to 0

Answer 4

can you help jdoe?

Answer 5

dunno

Answer 6

well, @Loser66 is correct thus far, you get the common factor out

Answer 7

$$
7tan^3(x)-21tan(x)=0 \implies 7tan(x)\pmatrix{tan^2(x)-3}=0
$$

Answer 8

to me, 7tan x (tan^2 x -3)=0 ---> tan x =0 or tan^2 x -3 =0

Answer 9

some more steps to get the answer

Answer 10

i got 0, pi/3, 2pi/3, pi, 4pi/3, 5pi/3

Answer 11

$$
7tan^3(x)-21tan(x)=0 \implies 7tan(x)\pmatrix{tan^2(x)-3}=0\\
\\
7tan(x)=0 \implies tan(x) = 0 \implies tan^{-1}(tan(x)) = tan^{-1}(0)\\
\implies \color{blue}{x = \text{the angle whose tangent is 0 } = \{0,\pi, 2\pi \}}\\
\\
tan^2(x)-3=0 \implies tan^{-1}\pmatrix{tan(x)}=tan^{-1}(\sqrt{3})\\
\implies \color{blue}{x = \text{the angles whose tangent is }\pm\sqrt{3}}
$$

Answer 12

so, check your Unit Circle for THOSE angles whose tangent is \(\pm\sqrt{3}\)

Answer 13

i think i got the right answer.

Answer 14

see i got another answer without the 0 and pi and it said it was wrong

Answer 15

hmm, yes, is those angles you listed already