Question

PLEASE HELP! WILL AWARD MEDAL/FAN!!((:
solve the equation in the indicated domain.
tanx+square root 3 =0 x E[0 degrees, 360 degrees)

Answer 1

The equation is this right?
\[\Large \tan(x) + \sqrt{3} = 0\]
I just want to be sure

Answer 2

yes!

Answer 3

I don't understand how to do this kind of problem.

Answer 4

The first thing to do is subtract `sqrt(3)` from both sides
\[\Large \tan(x) + \sqrt{3} = 0\]
\[\Large \tan(x) + \sqrt{3} - \sqrt{3} = 0 - \sqrt{3}\]
\[\Large \tan(x) = -\sqrt{3}\]

Answer 5

let me know when you have all this written down

Answer 6

I see. Okay.

Answer 7

So I'm left with tan(x) = - square root 3

Answer 8

we want the value of `x` all by itself, not the value of `tan(x)`

Answer 9

so inverse of tan?

Answer 10

so we apply the inverse tangent, or arctangent to both sides

Answer 11

`so inverse of tan?`
yes correct

Answer 12

use a calculator like this one

http://web2.0calc.com/

Answer 13

type in `arctan(-sqrt(3))`

Answer 14

i get -60...degrees...?

Answer 15

yep me too

Answer 16

is `-60 degrees` in the interval from 0 to 360 ?

Answer 17

...yes...?

Answer 18

no, it's not

0 to 360 is nothing but positive numbers (well except 0 itself)

Answer 19

...
but if it is negative, i thought it was going to be like 300 degrees

Answer 20

yeah you would add on 360 to -60 to get 300

Answer 21

-60 isn't in the interval

but 300 is

Answer 22

oh i see what you are saying
300 is positive, but -60 isn't, right? so -60 degrees isn't technically on the unit circle.

Answer 23

when they say ` x E[0 degrees, 360 degrees)` or \(\Large x \in [0^{\circ}, 360^{\circ})\) they want x to be in the interval from 0 to 360. Include 0 but exclude 360. You can have x equal to any number between 0 and 360. The value of x could be 0. The value of x cannot be 360.

Answer 24

there are infinitely many solutions to the equation you posted. But they are restricting the values of x which means we'll only get 2 solutions in this interval

Answer 25

Okay. I understand the open and closed parentheses concept.
Wait how do you know it's just going to be 2 solutions?

Answer 26

because tangent is negative in quadrant 2 and quadrant 4

the angle 300 degrees is in quadrant 4