Question

solve for x between 0 to 2pi
secx=2cscx

Answer 1

I can guide you through this, but I'll need your help
So first of all an always good starting point is to see if we can rewrite both trig functions
in terms of other trig functions

For example: cotg x can be rewritten as 1/tg x

Answer 2

If we can rewrite cotg x on that way,
how can we rewrite sec x on a similar way?

Answer 3

1/cosx=2(1/sinx)

Answer 4

To review: both sec x and csc x can be rewritten as
1/ another trig function
and those are ...

Answer 5

Yes, ur right

Answer 6

what is the next step?

Answer 7

And is there any other trig function that can be written in terms of both sin x and cos x?

Answer 8

sinx/cosx=tanx

Answer 9

Yerp! And is there any way we can pit together sin x and cois x at our equation
in order to get tan x?

Answer 10

sinx/cosx=2

Answer 11

tanx=2

Answer 12

Nice :)

Answer 13

And what would you do next?

Answer 14

arctan of 2

Answer 15

Mhm!

Answer 16

1.107

Answer 17

Is it right?

Answer 18

Yush!!!

Answer 19

so this is the answet?

Answer 20

Its right, but I think that there may still be other answers missing
if we have to think on tan x... so if we have to think on tan x as a function
what do you remember about it?

Answer 21

I have no clue

Answer 22

as you may remember the 3 main trig functions
(sin x, cos x and tan x) are all periodic functions
that is, the values each of them takes repeat every certain number of units
for example, for sin x values repeat every 2pi units
and therefore sin(pi)=sin(3pi)

Answer 23

tanx repeats every pi

Answer 24

And the same happenbs with cos x
every 2pi units too but tan x is a little but different
since it has some holes on it (I mean, we can't calculate tan(pi/2, for example)
and its values get repeated every pi units

so then, for example
tan(pi/4)=tan(5pi/4)

Answer 25

4.249

Answer 26

So then, if we know that for x=1.107 radians
tan x=2 which other value between 0 and 2pi can happen the same for?

Answer 27

Yes, 4.249 is correct. And is there any other possible value?
between 0 and 2pi?

Answer 28

can I subtract pi too

Answer 29

1.107-pi

Answer 30

Yes, you can and what would you get by doing so?

Answer 31

-2.034

Answer 32

right and is that between 0 and 2pi?

Answer 33

no.It is less than 0

Answer 34

can I add one more pi

Answer 35

4.249+pi

Answer 36

And what does that equal to?