Question

LAST ONE FOR THE NIGHT! Use a graph to solve the equation on the interval
[−2π, 2π].

tan x = - sqrt(3)

Answer 1

@satellite73

Answer 2

@Hero

Answer 3

@No.name

Answer 4

@dan815

Answer 5

Take the inverse tan of both sides

\(x = \tan^{-1}(-\sqrt{3})\)

Answer 6

You can do that to find one of the values. Afterwards add or subtract the period of tan to find the rest of the values.

Answer 7

my calculator says error

Answer 8

According to mine, there exists at least one value.

Answer 9

Make sure you are in radian mode and make sure you are entering the values correctly.

Answer 10

i am in radian mode. typing in \[\tan^-1(-\sqrt{3})\]

Answer 11

You have to type \(\tan^{-1}(-\sqrt{3})\) precisely with no mistakes.

Answer 12

that is exactly what I am typing in. let me try my online calculator

Answer 13

What calc do you own?

Answer 14

TI 83

Answer 15

is it -pi/3?

Answer 16

Put it this way, I have three different TI-calculators and I used all three of them and they all give me the same result. Yes -pi/3 is one of the values.

Answer 17

is that our first interval? or our base?

Answer 18

That's the starting point. Now add and subtract the appropriate periods of tan to find the rest of the values.

Answer 19

subtract -2pi and add 2pi to -pi/3?

Answer 20

What is the period of the tan function?

Answer 21

Please answer the question first.

Answer 22

isn't the period the 3 or sqrt(3)

Answer 23

No, the period of the tangent function is \(\pi\). So keep adding and subtracting \(\pi\) from \(-\frac{\pi}{3}\) until you have all the values \(-2\pi\) < x < \(2\pi\)

Answer 24

subtracting pi from -pi/3?

Answer 25

subtract 5/3pi till -2pi

Answer 26

Yes, that's right. You have to go in both directions because you have to find every value up to \(-2\pi\)

Answer 27

You have to keep subtracting \(\pi\)

Answer 28

add 7/3pi

Answer 29

interval = -5/3pi, 7/3pi ???

Answer 30

You're confusing yourself. I can feel it

Answer 31

Keep adding and subtracting \(\pi\) only

Answer 32

Right, these are my equations:
-pi/3+pi(x)=2pi
-pi/3-pi(x)=-2pi

Answer 33

Once you find a positive value, add \(\pi\) to find the next value. Once you find a negative value, subtract \(\pi\) again to find the next value. You're supposed to find the values between -2\(\pi\) and 2\(\pi\) not set an equation equal to them.

Answer 34

Im confused now. I am not sure what you mean. I thought you wanted to see how many pies we subtract from 5/3pi till you get -2pi. Then see how many pies we add to 5/3pi till you get 2pi.

Answer 35

I would be incredibly grateful if you could give me the answers and then work from there?

Answer 36

We found \(x = -\dfrac{\pi}{3}\). So we keep adding or subtracting \(\pi\) from that until we get to \(\pm 2\pi\).

Answer 37

it does say "use a calculator" right?

Answer 38

it says use a graph

Answer 39

http://www.wolframalpha.com/input/?i=tan+%28x+%29%3D+-+sqrt%283%29

Answer 40

@Hero which is 7/3pi to get to 2pi

Answer 41

@satellite73 that does not give us intervals

Answer 42

so i am still doing this wrong?

Answer 43

http://www.wolframalpha.com/input/?i=tan+%28x+%29%3D+-+sqrt%283%29%2C+-2pi+%3C+x+%3C+2pi

Answer 44

well Hero cleared that up for me ty

Answer 45

I meant to post this for a graph:
https://www.desmos.com/calculator/dzd5suoweu

Answer 46

The solutions occur where the red and green intersect if you know how to read the graph.