How Do You Determine CscØ with CosØ and TanØ?

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SUMMARY

The discussion focuses on determining the value of cscØ given cosØ = 1/2 and a negative tanØ. It establishes that cscØ is the reciprocal of sinØ, and since cosØ is positive, sinØ must be negative. Using the Pythagorean identity sin²Ø + cos²Ø = 1, the value of sinØ is derived as -√(3/4), leading to cscØ = -2/√3 or -2√3/3. The final conclusion is that the correct answer is option d) -2√3/3.

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  • #31
arildno said:
BTW, the positive square root of 3/4 may be written as follows:
\sqrt{\frac{3}{4}}=\frac{\sqrt{3}}{\sqrt{4}}=\frac{\sqrt{3}}{2}
So then the answer would be -1/ \sqrt{\frac{3}{2}?

But again, something seems wrong.
 
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  • #32
Why don't you think it is right?
It is; however, why are you dissatisfied with it?
(It is important when trying to learn maths to express your own ideas/doubts, otherwise other persons won't be able to show you the right way in a manner you understand/are satisfied with)
 
  • #33
Poweranimals said:
So then the answer would be -1/ \sqrt{\frac{3}{2}?
Certainly, this can be simplified as:
csc\phi=\frac{-1}{\frac{\sqrt{3}}{2}}=-\frac{2}{\sqrt{3}}
 
  • #34
Wouldn't it be -2 square root of 3/3?
 
Last edited:
  • #35
Isn't that what I wrote?
Besides, I just saw that you wrote in post 31 that
"So then the answer would be \frac{-1}{\sqrt{\frac{3}{2}}} ?
This is wrong; it should be:

\frac{-1}{\frac{\sqrt{3}}{2}}
 
  • #36
Poweranimals said:
Wouldn't it be -2 square root of 3/3?
What do you mean by this??
The answer is, again:
csc\phi=-\frac{2}{\sqrt{3}}
EDIT:
Yes, you can write this as:
csc\phi=-\frac{2}{\sqrt{3}}=-\frac{2\sqrt{3}}{3}<br />
 
Last edited:
  • #37
Yeah, I meant to write something else, but I kept screwing up the code. Anyway, what you have looks different from what I had, so I got confused.
 
  • #38
I think we're finally landed together here..
At least if you read my previous post..
 
  • #39
arildno said:
What do you mean by this??
The answer is, again:
csc\phi=-\frac{2}{\sqrt{3}}
EDIT:
Yes, you can write this as:
csc\phi=-\frac{2}{\sqrt{3}}==-\frac{2\sqrt{3}}{3}<br />
Well, judging by the multiple choice answers, the options are:

a) 2, b) -2, c) 2 and sqare root of 3/3, and d) -2 and the square root of 3/3. Meh, I could just guess, but I wouldn't really learn anything; and I've got a test on it tonight.
 
  • #40
As you see, my edit shows that alternative d) is what you should choose! :smile:

I'm sorry, I don't understand your wording of c) and d)
They're unclear!

I believe it is d) you're after
 

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