Question

which of the following is equivalent to 2csc(2x)?
a. csc(x)
b. sec(x)
c. csc(x) sec(x)
d. sin(x) cos(x)

Answer 1

looky looky identity
there are only two things you need to recall here, really, apart from the more obvious ones... things like
\[\large \csc\theta = \frac1{\sin\theta}\]\[\large \sec\theta = \frac1{\cos\theta}\]

just remember that
\[\large \sin(2\theta) = 2\sin(\theta)\cos(\theta)\]

Answer 2

hmm

Answer 3

I'm feeling d., but is there a way to break it down?

Answer 4

while I'd normally say trust your feelings, this is not the time for that :D
I don't actually know ^.^

Answer 5

hmm

Answer 6

well, sin 2x=2 sin x cos x

Answer 7

so would csc 2x= 1/2 sin x cos x?

Answer 8

well naturally ;)

Answer 9

so the 2csc would equal...

Answer 10

hmm

Answer 11

multiply the whole expression by 2?

Answer 12

yup

Answer 13

so...

Answer 14

that would still be 1/2 sin x cos x

Answer 15

nopity nope :>

Answer 16

well

Answer 17

2/4 sin x cos x=1/2 sin x cos x

Answer 18

don't be silly :P
when you multiply a fraction by a number, you only multiply it with the numerator XD

Answer 19

ahh

Answer 20

so 2/2 sin x cos x?

Answer 21

sin x cos x?

Answer 22

wait

Answer 23

or 1/sin x cos x

Answer 24

what does your heart tell you?

Answer 25

1/ sin x cos x

Answer 26

\[\Large \frac1{\sin(x)\cos(x)}= \frac1{\sin(x)}\cdot \frac1{\cos(x)}\]

Answer 27

which is 1/ sin(x) cos(x)

Answer 28

which is csc (x)

Answer 29

right?

Answer 30

how?

Answer 31

well... it can't be sin(x) cos(X) since our answer is 1/sin(x) cos(x)

Answer 32

so how is it csc(x)

Answer 33

because sin(x)= sin(x)(cos x)...

Answer 34

cause sin 2x= 2 sin x cos x

Answer 35

that's rich XD

Answer 36

sin2x = 2sinxcosx granted
but I don't see how that means
\[\Large \frac1{\sin(x)\cos(x) }= \csc(x)\]

Answer 37

what I moment...

Answer 38

the derp moment is coming...

Answer 39

csc(x) sec(x)?

Answer 40

cause that would equal 1/sin x times 1/sec x

Answer 41

and that is the right answer I think

Answer 42

Of course it is.
You really need to practice :/

Answer 43

but dude, I wish my teacher would be more clear. He is Asian and he has

trouble speaking English :(

Answer 44

I also took trig online

Answer 45

I would probably learn more if I had a teacher like you

Answer 46

by the way, could you help me with one more problem?

Answer 47

aww.. I'm part Asian :|

Answer 48

and okay, but you're taking the lead with that problem :P

Answer 49

the lead?

Answer 50

Only occasional hints from me... ok?
that way you learn :)

Answer 51

ahh, lol

Answer 52

could you help me with one more problem?

Answer 53

go ahead

Answer 54

you got a medal :)