Question

solve the equation sec(θ)csc(θ)=2csc(θ) pls show steps

Answer 1

use this http://www.wolframalpha.com/input/?i=sec%28%CE%B8%29csc%28%CE%B8%29%3D2csc%28%CE%B8%29

Answer 2

divide = csc(x)
sec(x) = csc(x)
1/sin(x) = 1/cos(x)
sin(x) = cos(x)
This is at 45degrees, and 225 degres

Answer 3

Telling people to use wolfram alpha teaches nothing.

Answer 4

they can see the whole stuff dear pk51. I understand it better with graphs and stuff. In any case, this is why many of us post answers

Answer 5

trig gives me headaches no joke.

Answer 6

when you divide by a trig function like that, just make sure you arent accidentally deleting one of the solutions. otherwise, nice nice. :)

Answer 7

\[\sec(\theta)\csc(\theta)-2\csc(\theta)=0\]
\[\csc(\theta)(\sec(\theta)-2)=0\]

Answer 8

secx*cscx = 2cscx
cosx*sinx = 1/2 *sinx
2sinx*cosx = sinx
2sinx*cosx - sinx = 0
sinx*(2cosx - 1) = 0

this gives sinx = 0 which is 0 or pi
2cosx - 1 = 0
cosx = 1/2
x = pi/3 or -pi/3

Answer 9

joe i still do that sometimes and forget what i'm doing
its the same reaon for if we have x^2=x
if we divide both sides by x we are losing a solution
x=1

Answer 10

i got yelled at for making that mistake last semester lol. I'll never forget again >.<

Answer 11

lol

Answer 12

something about my solution is off....i guess i cant just flip all the functions? since its undefined if i do that?

Answer 13

and lol >.< people cant take criticism =/ it was someone on here?

Answer 14

yes

Answer 15

wow this is like chinese to me what identities did you use because i dont recoginse it.

Answer 16

do you know the ones like this?
\[\sec(\theta) = \frac{1}{\cos(\theta)}, \csc(\theta) = \frac{1}{\sin(\theta)}\]

Answer 17

here it was fine to divide by cscx since cscx is never zero :)

Answer 18

\[\csc(\theta)(\sec(\theta)-2) = 0 \iff \csc(\theta) = 0, \sec(\theta)-2 = 0\]

Answer 19

ah, cool cool, i see now.

Answer 20

yes joe i do

Answer 21

So at first i was trying to use those rules, but i ended up creating extra solutions by accident O.o the horror!

Answer 22

but now i see, so csc can never be 0, so that means:
\[\sec(\theta) - 2 = 0 \iff \sec(\theta) = 2 \iff \cos(\theta) = \frac{1}{2} \iff \theta = \frac{\pi}{6}, -\frac{\pi}{6}\]

Answer 23

er...over 3, not 6 >.<

Answer 24

\[\frac{π}{3},−\frac{π}{3}\]

Answer 25

very nice drawing!

Answer 26

:)

Answer 27

i should had drawn her eating a duck

Answer 28

i didnt know you could draw o.O

Answer 29

myininaya that was excellent thx everyone too.

Answer 30

i'm limited in my drawingness

Answer 31

not as limited as i am lol >.< im only good at drawing ducks that look like birds.

Answer 32

lol

Answer 33

ok i gotta go take care of my cat for a few seconds

Answer 34

alright, lates :P

Answer 35

thx

Answer 36

np