anonymous
  • anonymous
Find cot θ if csc θ = square root5/2and tan θ > 0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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ybarrap
  • ybarrap
What do you know about \(\csc \theta\) and \(\cot\theta\) with respect to a right triangle?
anonymous
  • anonymous
Could you use the pythagorean identities?
ybarrap
  • ybarrap
yes

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ybarrap
  • ybarrap
Can you draw a picture that shows csc θ = square root5/2? Let's start with that.
anonymous
  • anonymous
|dw:1378142919615:dw| Sorry Idk if I'm doing this right.
ybarrap
  • ybarrap
Let's start with that. |dw:1378143208841:dw| \(\Large\csc\theta={1\over \sin\theta}\). So \(\Large \sin\theta={1\over \csc\theta}\) . How do we find \(\Large \cos\theta\)?
ybarrap
  • ybarrap
\(\cos\theta \) should have been \(\sin \theta\) |dw:1378143498230:dw|
ybarrap
  • ybarrap
So now to get the third side, use pythagoras theorem.
ybarrap
  • ybarrap
That will be also be \(\cos\theta\).
ybarrap
  • ybarrap
Make sense?
ybarrap
  • ybarrap
|dw:1378143697956:dw|
ybarrap
  • ybarrap
any questions?
anonymous
  • anonymous
So I add 2/squareroot5+2 squareroot5?
ybarrap
  • ybarrap
We know that \(x^2+y^2=c^2\), we have \(y=2/\sqrt 5/\) already and 1 (i.e. c) from our initial equation: \(1\csc\theta=\sqrt5 /2\). So now to get x, we have \(x=\sqrt{c^2 -y^2}\), where we then get that \(x=\sqrt 5/5\). But this is also \(\cos\theta\).
anonymous
  • anonymous
OHHH I see! Omg I didn't even see that you edited the above triangle. Thanks!
ybarrap
  • ybarrap
Now we have \(\sin\theta\) and \(\cos\theta\) . How can we write \(\tan\theta\) in terms of \(\sin\theta\) and \(\cos\theta\)?
anonymous
  • anonymous
tan u= 1/cot u
anonymous
  • anonymous
Wait: tan u= sinu/cos u
ybarrap
  • ybarrap
Same type of question, how can you write \(\cot\theta\) in terms of \(\cos\theta \) and \(\sin\theta\)?
ybarrap
  • ybarrap
ok, now we have both of those, just divide one (the right one) by the other and you have your answer.
anonymous
  • anonymous
I got 2
ybarrap
  • ybarrap
close, what are you dividing by what?
ybarrap
  • ybarrap
you need cot, not tan.
anonymous
  • anonymous
2/squareroot5/squareroot5/5
anonymous
  • anonymous
ohhh so 1/2 then
ybarrap
  • ybarrap
Yeah, you had \(\tan\theta=\dfrac{\sin\theta}{\cos\theta}\). So ans is 1/2
anonymous
  • anonymous
Okay, I get it! Thanks for having the patience to help me figure out the answer!
ybarrap
  • ybarrap
I like that you also have the patience. Let me know if you need any more help.
anonymous
  • anonymous
Okay! thanks again! :)
ybarrap
  • ybarrap
yw - good luck!

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