Question

tan^3(X)= 1/3tan(x)

Answer 1

\(\bf tan^3(x)=\cfrac{1}{3tan(x)}\implies tan(x)tan^3(x)=\cfrac{1}{3}\)

then just solve for "tan(x)" and get \(\bf tan^{-1}\) to both sides

Answer 2

@sqadir Is it like that, or\[\tan^3(x)=(1/3)\tan(x)\]

Answer 3

yes

Answer 4

i need to find the exact solutions

Answer 5

the one johnny was talking about

Answer 6

\(\bf tan^3(x)=\cfrac{1}{3}tan(x)\implies \cfrac{tan^3(x)}{tan(x)}=\cfrac{1}{3}\)

then solve for "tan(x)" and then get \(\bf tan^{-1}\) to both sides

Answer 7

no the question is Solve the following equation, giving the exact solutions which lie in [0, 2π). (Enter your answers as a comma-separated list.)

Answer 8

right, I got that

Answer 9

i dont see where you got that

Answer 10

i need more one more answer for this

Answer 11

so... just solve for "tan(x)"... what would you get?

Answer 12

im not sure

Answer 13

0, pi,

Answer 14

well... what would we get for \(\bf \cfrac{tan^3(x)}{tan(x)}\quad ?\)

Answer 15

any like-term to be cancelled there?

Answer 16

tan^3(x)

Answer 17

It would be 3tan^3(x)/tan(x).

Answer 18

ohhh

Answer 19

and then?

Answer 20

h... actually lemme take ... a quick turn

Answer 21

ok

Answer 22

and let it equal 1.

Answer 23

how

Answer 24

\(\bf tan^3(x)=\cfrac{1}{3}tan(x)\implies tan^3(x)-\cfrac{1}{3}tan(x)=0\\ \quad \\
\textit{getting common factor, we get}\\ \quad \\
tan(x)\left[tan^2(x)-\cfrac{1}{3}\right]=0\)

Answer 25

how do find the exact solutions though?

Answer 26

so we end up with ... say 2 roots, noticeable up there

Answer 27

\[\tan^3(x)=(1/3)\tan(x)\rightarrow 3\tan^3(x)=\tan(x)\rightarrow (3\tan(x))/\tan(x)=1\]

Answer 28

\(\bf tan^3(x)=\cfrac{1}{3}tan(x)\implies tan^3(x)-\cfrac{1}{3}tan(x)=0\\ \quad \\
\textit{getting common factor, we get}\\ \quad \\
tan(x)\left[tan^2(x)-\cfrac{1}{3}\right]=0\implies

\begin{cases}
tan(x)=0\\ \quad \\
\bf tan^2(x)-\cfrac{1}{3}=0
\end{cases}\)

Answer 29

see the 2 answers?

Answer 30

that is not correct according to my online assignment

Answer 31

Solve the following equation, giving the exact solutions which lie in [0, 2π). (Enter your answers as a comma-separated list.)

Answer 32

the answers have to be between 0 and 2pi

Answer 33

@jdoe0001 , what value of tan(x) gives you 1/3? From the unit circle.

Answer 34

\(\begin{cases}
tan(x)=0\implies tan^{-1}[tan(x)]=tan^{-1}(0)\implies x=tan^{-1}(0)\\ \quad \\
tan^2(x)-\cfrac{1}{3}=0\implies tan^2(x)=\cfrac{1}{3}\implies tan(x)=\sqrt{\cfrac{1}{3}}\\ \quad \\
\implies tan(x)=\cfrac{\sqrt{1}}{\sqrt{3}}\implies tan(x)=\cfrac{1}{\sqrt{3}}\\ \quad \\
\implies tan^{-1}[tan(x)]=tan^{-1}\left(\cfrac{1}{\sqrt{3}}\right)\implies x=tan^{-1}\left(\cfrac{1}{\sqrt{3}}\right)
\end{cases}
\)

Answer 35

can you explain all of this

Answer 36

.... ok... what part?

Answer 37

everything and where is the answer

Answer 38

the answers have to have pi in them

Answer 39

the answer comes from getting the \(tan^{-1}\) from both sides

Answer 40

@JonnyVonny well, it won't be 1/3, it'd be \(\cfrac{1}{\sqrt{3}}\)

Answer 41

the answers are angles, inverse trigonometric functions return an angle, thus

Answer 42

@arthur_ser that is not correct according to the grader