anonymous
  • anonymous
If sin theta=3/5 and theta is in quad 2 the exact form of csc (pi/2-theta) is...? Just want to make sure if this works??
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
sinθ = 3/5 csc(π/2 - θ) = secθ = 1/cosθ = -4/5
triciaal
  • triciaal
|dw:1436736243879:dw|
triciaal
  • triciaal
given sin = 3/5 and in quad 2

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anonymous
  • anonymous
@triciaal So what does that mean?
triciaal
  • triciaal
csc = 1/sin = hypotenuse / opposite 5/-4
anonymous
  • anonymous
The answer is -5/4 then?
triciaal
  • triciaal
|dw:1436737161908:dw|
anonymous
  • anonymous
What do I do with that?
triciaal
  • triciaal
your question "the exact form of csc (pi/2-theta) is?"
triciaal
  • triciaal
shouldn't it be between -1 and 1 only?
freckles
  • freckles
"sinθ = 3/5 csc(π/2 - θ) = secθ = 1/cosθ = -4/5" in your work here the only mistake you made was not flipping -4/5 that cos(theta)=-4/5 so 1/cos(theta) is the reciprocal of that
triciaal
  • triciaal
csc = hypotenuse/ opposite
ybarrap
  • ybarrap
|dw:1436737547332:dw| However, since we are in the 2nd quadrant $$ -\csc\left (\frac{\pi}{2}-\theta\right )=\frac{{\bf\color{red}{-}}5}{~~4} $$ Note the negative corresponding to the value of \(x\) in the 2nd quadrant.
triciaal
  • triciaal
@zepdrix why/when is the value < -1 in general?
zepdrix
  • zepdrix
Trish :) Maybe you're thinking about sine and cosine, which have restricted output values between 1 and -1
zepdrix
  • zepdrix
That's the only way they will satisfy a triangle `hypotenuse longer than other sides`\[\large\rm \sin \theta=\frac{opposite}{hypotenuse}=\frac{shorter}{longer}\lt1\]But for Cosecant, I guess we have the reverse going on, ya? We always need to be 1 or larger.\[\Large\rm \csc \theta=\frac{hypotenuse}{opposite}=\frac{longer}{shorter}\gt1\]
ybarrap
  • ybarrap
Does this make sense? |dw:1436738761632:dw|
triciaal
  • triciaal
@zepdrix thanks just never thought about it @ybarrap thanks for the CAST diagram but I was checking the limit ; not if positive or negative
triciaal
  • triciaal
@ybarrap no tan on your chart
ybarrap
  • ybarrap
|dw:1436739672137:dw|
anonymous
  • anonymous
Sorry guys I'm back! So i think I got the answer this time around! @triciaal @zepdrix
anonymous
  • anonymous
-1/3/5 I think @zepdrix @triciaal @freckles
freckles
  • freckles
what is that the answer to?
freckles
  • freckles
are you looking at a new question?
anonymous
  • anonymous
No for the one I put on
freckles
  • freckles
oh I guess you didn't understand what anyone posted :p
anonymous
  • anonymous
Yeah nothing at all XD
anonymous
  • anonymous
This is the only question I can't get!! :////
freckles
  • freckles
ok let's start from the beginning this shouldn't be long at all
freckles
  • freckles
"sinθ = 3/5 csc(π/2 - θ) = secθ = 1/cosθ = -4/5" do you remember this is what you first posted here?
freckles
  • freckles
this was your first try here anyways
anonymous
  • anonymous
Yeah thats what I did, but I figured it was wrong
freckles
  • freckles
it is a little wrong
freckles
  • freckles
the first part is totally awesome
freckles
  • freckles
the second part the part where you say 1/cos(theta)=-4/5 is a little off
freckles
  • freckles
yes cos(theta)=-4/5 but what is 1/cos(theta)=?
freckles
  • freckles
if I tell you a=2/5 then what is 1/a=?
freckles
  • freckles
or how about this if I tell you 1/a=5/2 then a=?
freckles
  • freckles
a and 1/a are reciprocals of one another that means they are the "flippings of each other" like 2 and 1/2 are reciprocals and 2/5 and 5/2 are reciprocals and -2/5 and -5/2 are reciprocals
freckles
  • freckles
so if I say a=2/5 then 1/a=5/2 or if I say 1/a=5/2 then a=2/5
freckles
  • freckles
so if cos(theta)=-4/5 then 1/cos(theta)=?
freckles
  • freckles
if you want to replace cos(theta) with a you can if a=-4/5 then 1/a=?
anonymous
  • anonymous
@freckles Alright I think I need a little bit to take this all in cuz you just shot me a whole bunch of stuff at me XD I think I get what your saying let me see what I can do
freckles
  • freckles
take your time
anonymous
  • anonymous
Wait so would it be -5/4 then??? *fingers crossed right now that its right** haha
freckles
  • freckles
yes yes !!!
anonymous
  • anonymous
YYAYYY!!
freckles
  • freckles
-5/4 is indeed the reciprocal of -4/5
anonymous
  • anonymous
So where do you go on from there? Is there more to be done??
freckles
  • freckles
nope
anonymous
  • anonymous
Ohmygod that simple for a question like this? My mind is just blown right now .... XD
freckles
  • freckles
\["\sinθ = 3/5 \\ \csc(π/2 - θ) = \secθ = 1/\cosθ = -4/5" \\ \text{ so the correcting your work would look like this: } \\ \csc(\frac{\pi}{2}-\theta)=\sec(\theta)=\frac{1}{\cos(\theta)}=\frac{1}{\frac{-4}{5}}=\frac{-5}{4}\]
freckles
  • freckles
by the way you know that first thing you used it called a cofunction identity most people forget that one so you are doing awesome!
anonymous
  • anonymous
@freckles Thanks again seriously!! Haha really helped! Literally am beating myself up not knowing lol
freckles
  • freckles
i think we were all working on our algebra in trig and even in calculus
freckles
  • freckles
algebra/arithemetic
freckles
  • freckles
and/or
freckles
  • freckles
guess what you are going to have to know so much algebra for calculus you are going to think you never learned algebra :p well that has been my experience with some anyways I'm kind a kidding. I know you are going do okay especially since you can always get help if you need it.
anonymous
  • anonymous
Haha true!! thanks again! I know with Calc I am going to need lots of help especially!!
triciaal
  • triciaal
math is fun just takes lots of practice

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