Question

if cscx=2 and x is in quadrant 2 then sin(2x)=

Answer 1

what is csc ?

Answer 2

I need to know what you know so I can help you properly

Answer 3

csc = 2
csc= 1/sin
uhh I dont really have any other info

Answer 4

oh and it would be hypotenuse/opposite

Answer 5

okay, csc is the inverse of sin
like you said \(csc = \large \frac{1}{sin} \)

Answer 6

Yes

Answer 7

so it is possible to think it like
\(\large \frac{1}{sin~x} = 2 \)

Answer 8

so if that is possible, it is also possible to think of other trigonometric identities. yes?

Answer 9

Yes I think so

Answer 10

so tell me, what other trigonometric identities do you know or you're familiar with

Answer 11

sin(2x)=2sinxcosx
and I think that is important to know in this equation

Answer 12

I used the wrong word. I said inverse, when I meant to use RECIPROCAL.

Answer 13

YES! you can use something like that

Answer 14

its okay same thing basically?
Okay well I am not seeing how it can be used, I just though it would fit since we have the sin(2x)=

Answer 15

so basically cscx=1/2sinxcox

Answer 16

which leads me to thinking that sin(2x)=1/2 when cscx=2

Answer 17

cosx*

Answer 18

does the word quadrant ring any bell?

Answer 19

yes, and in the second quadrant- isnt everything positive?

Answer 20

hmm?

Answer 21

Oh, wait sin is positive and cos is negative

Answer 22

so then sin(2x)= -1/2 ??

Answer 23

don't be confused okay?
isn't sin your y also
cos is x
this is why
tan = sin/cos = y/x = slope

Answer 24

Yes I know this.

Answer 25

so csc=1/x

Answer 26

are you thinking like this?
1/x = 2
x = 1/2
so
\(sin ~(2 \large \frac{1}{2}) = \)

Answer 27

ohhh i see. I didn't think that far ahead. Thanks then. So now we just do (2)(1/2) which is 1

Answer 28

sorry my connection keeps lagging

Answer 29

so sin(1)??

Answer 30

alright, now I am slightly lost.

Answer 31

do not be lost
this just requires some practice of fiddling with trig identities and being really familiar with them

Answer 32

okay well now what can we do using the sin(1)

Answer 33

I am actually stuck now, what can I do?

Answer 34

google brought up:
https://answers.yahoo.com/question/index?qid=20130805043703AAfAth7
which has the solution