How Do You Determine CscØ with CosØ and TanØ?

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Homework Help Overview

The discussion revolves around determining the value of cscØ using the given values of cosØ and tanØ. The subject area includes trigonometric identities and relationships between sine, cosine, and tangent functions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationships between cscØ, sinØ, tanØ, and cosØ. Questions arise regarding how to derive sinØ from the known values of cosØ and tanØ, as well as the implications of the signs of these functions in different quadrants.

Discussion Status

The discussion is ongoing with participants attempting to clarify their understanding of trigonometric identities. Some guidance has been provided regarding the relationships between the functions, but there is no explicit consensus on the final value of cscØ.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There is also a focus on understanding the signs of the trigonometric functions based on the given conditions.

  • #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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