Question

Can someone please help? tan(x/2)=(sqrt3)/3

Answer 1

\[\large\rm 0.5x= tan^{-1}\frac{√3}{3} \]

Answer 2

But for what intervals are you finding the values of x?

Answer 3

lt doesnt say the options are x=2pi/3 +pi.....x=pi/3+2npi......x=7pi/6+npi and 11pi/6 + npi....x=5pi/3+npi......x=5pi/6+npi and 7pi/6+npi..........All where n is an integer

Answer 4

i need help bro

Answer 5

@freckles please

Answer 6

please

Answer 7

i need help

Answer 8

\[\tan(\frac{x}{2})=\frac{\sqrt{3}}{3} \\ \text{ \let }\theta=\frac{x}{2} \\ \text{ do you know how to solve } \\ \tan(\theta)=\frac{\sqrt{3}}{3} \\ \text{ also know as } \\ \tan(\theta)=\frac{1}{\sqrt{3}}\]

Answer 9

whip out your unit circle and find when sin is 1/2 and cos is sqrt(3)/2

find also when sin is -1/2 and cos is -sqrt(3)/2

Answer 10

once we find theta
we will go back and find x

Answer 11

pi/6 and 5pi/6.....7pi/6 and 11pi/6

Answer 12

well at 11pi/6 and 5pi/6 you have tan is negative

this is why I asked you to look only at the positive, positive quadrant and the negative, negative quadrant

that is the ordered pairs (sqrt(3)/2,1/2) and (-sqrt(3)/2,-1/2) belong to those quadrants I just mentioned

Answer 13

so we will use
\[\theta=\frac{\pi}{6} +2n \pi \\ \text{ or } \\ \theta=\frac{7\pi}{6}+2n \pi\]

Answer 14

recall the equation to solve want tan(x/2)=sqrt(3)/3
but we replaced x/2 with theta

Answer 15

so you have to solve the following two equations for x:
\[\frac{x}{2}=\frac{\pi}{6}+2n \pi \\ \frac{x}{2}=\frac{7\pi}{6}+2n \pi\]

Answer 16

hmm

Answer 17

never learned that. how do u solve it?

Answer 18

It is basic fractions

Answer 19

pi/3?

Answer 20

sorry it is super late

Answer 21

so you never solved equations like x/2=6
?

Answer 22

you multiply both sides by ...

Answer 23

2

Answer 24

also I could have condensed my equations into one equation

Answer 25

yes

Answer 26

@freckles Are you sure the equations to which you simplified are correct since there's no mention of the answer derived through them in the choices

Answer 27

my answer is correct
however I just mentioned that I could condense my two equations into one equation

Answer 28

\[\frac{x}{2}=\frac{\pi}{6}+n \pi\]

since the line segment from (sqrt(3)/2,1/2) and (-sqrt(3)/2,-1/2) has an angle of 180 degrees

Answer 29

anyways yes you just must multiply both sides by 2