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# C3 trig watch

1. Why are you allowed to divide by cosx here when cosx could = 0, as the domain is between 0 and 2pi ???

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2. (Original post by anoymous1111)
Why are you allowed to divide by cosx here when cosx could = 0, as the domain is between 0 and 2pi ???

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You're not.
3. You can divide by because isn't a solution. You're not allowed to divide by cos x when you can factor it out, if you can't factor it out, then divide through by all means.
4. (Original post by Zacken)
You can divide by because isn't a solution. You're not allowed to divide by cos x when you can factor it out, if you can't factor it out, then divide through by all means.
How do you know that cosx = 0 isn't a solution?

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5. (Original post by anoymous1111)
How do you know that cosx = 0 isn't a solution?

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It's like having 3x +2 = -x, and then saying x=0 is a solution.

When then you need for the RHS = LHS and make cos x = 0 a solution, but cos x = 0 doesn't make 3 sin x = 0 a solution.
6. (Original post by Zacken)
It's like having 3x +2 = -x, and then saying x=0 is a solution.

When then you need for the RHS = LHS and make cos x = 0 a solution, but cos x = 0 doesn't make 3 sin x = 0 a solution.
Is that because sinx and cosx never equal 0 for the same value of X?

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7. It's because, you aren't really loosing the cos, you're converting it to tan instead, so you're still conserving the cos solutions
8. (Original post by JohnnyDavidson)
It's because, you aren't really loosing the cos, you're converting it to tan instead, so you're still conserving the cos solutions
Really? Ok

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9. (Original post by JohnnyDavidson)
It's because, you aren't really loosing the cos, you're converting it to tan instead, so you're still conserving the cos solutions
Is my reply correct in post 7?

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10. (Original post by JohnnyDavidson)
It's because, you aren't really loosing the cos, you're converting it to tan instead, so you're still conserving the cos solutions
Is what this person says true about being able to divide if both sides can't equal 0 at any given angle?

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11. (Original post by anoymous1111)
Is my reply correct in post 7?

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Yups.
12. (Original post by anoymous1111)
Is my reply correct in post 7?

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Yes - whenever you have acos x = bsin x for some constants a and b then you can divide by cos x (or sin x) because there are no angles x which have cos x = sin x = 0
13. (Original post by davros)
Yes - whenever you have acos x = bsin x for some constants a and b then you can divide by cos x (or sin x) because there are no angles x which have cos x = sin x = 0
Thank you!

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14. (Original post by anoymous1111)
Why are you allowed to divide by cosx here when cosx could = 0, as the domain is between 0 and 2pi ???

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Unfortunately, some of the answers here only give explanations that work in the very particular context in involving ... sin(x) = ... cos(x) and the fact that sin and cos cannot equal zero simultaneously; ... whilst this is true in the context, it does not answer your original question (needless to say there are many contexts when dividing an equation by cos x may be desirable).

The reality is that many texts, especially uk text books, tend to be very, very slack and lazy when defining mathematical concepts.

In the true sense, to claim that tan(x)= sin(x) / cos(x) is not quite correct.

to claim that tan(x)=sin(x) / cos(x) where x can be any real number with the exception that x cannot = 90 + n180, where n is an integer is correct..

hmmm, I should have typed that in Latex really, but tired...
15. (Original post by dpm)
Unfortunately, some of the answers here only give explanations that work in the very particular context in involving ... sin(x) = ... cos(x) and the fact that sin and cos cannot equal zero simultaneously; ... whilst this is true in the context, it does not answer your original question (needless to say there are many contexts when dividing an equation by cos x may be desirable).

The reality is that many texts, especially uk text books, tend to be very, very slack and lazy when defining mathematical concepts.

In the true sense, to claim that tan(x)= sin(x) / cos(x) is not quite correct.

to claim that tan(x)=sin(x) / cos(x) where x can be any real number with the exception that x cannot = 90 + n180, where n is an integer is correct..

hmmm, I should have typed that in Latex really, but tired...
That makes much more sense! Thanks a lot

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16. (Original post by dpm)
Unfortunately, some of the answers here only give explanations that work in the very particular context in involving ... sin(x) = ... cos(x) and the fact that sin and cos cannot equal zero simultaneously; ... whilst this is true in the context, it does not answer your original question (needless to say there are many contexts when dividing an equation by cos x may be desirable).

The reality is that many texts, especially uk text books, tend to be very, very slack and lazy when defining mathematical concepts.

In the true sense, to claim that tan(x)= sin(x) / cos(x) is not quite correct.

to claim that tan(x)=sin(x) / cos(x) where x can be any real number with the exception that x cannot = 90 + n180, where n is an integer is correct..

hmmm, I should have typed that in Latex really, but tired...
There's nothing wrong with most of the explanations given above and they do answer the 'original question', because the 'original question' was precisely about a specific equation!

Those values for which tan x is undefined are precisely the values for which cos x = 0, so if you know that cos x can't be zero - as we do in the 'original question' - then it's perfectly valid to divide by cos x and assert that tan x = sin x / cos x.
17. (Original post by davros)
There's nothing wrong with most of the explanations given above and they do answer the 'original question', because the 'original question' was precisely about a specific equation!

Those values for which tan x is undefined are precisely the values for which cos x = 0, so if you know that cos x can't be zero - as we do in the 'original question' - then it's perfectly valid to divide by cos x and assert that tan x = sin x / cos x.
Not according to my view of the topic.
The original question was, and I quote:
"Why are you allowed to divide by cosx here when cosx could = 0, as the domain is between 0 and 2pi ???"

this is the precise question that I answered. Precisely.

That not withstanding, the point I make regarding the general appalling way that concepts are portrayed in so many texts stands.

** The op seemed to appreciate the little extra added, so that's good enough for me.
18. (Original post by dpm)
Not according to my view of the topic.
The original question was, and I quote:
"Why are you allowed to divide by cosx here when cosx could = 0, as the domain is between 0 and 2pi ???"

this is the precise question that I answered. Precisely.

That not withstanding, the point I make regarding the general appalling way that concepts are portrayed in so many texts stands.

** The op seemed to appreciate the little extra added, so that's good enough for me.
It's not. Note the use of the word here that the OP explicitly used to refer to the problem that she posted in the second post.
19. (Original post by dpm)
Not according to my view of the topic.
The original question was, and I quote:
"Why are you allowed to divide by cosx here when cosx could = 0, as the domain is between 0 and 2pi ???"

this is the precise question that I answered. Precisely.

That not withstanding, the point I make regarding the general appalling way that concepts are portrayed in so many texts stands.

** The op seemed to appreciate the little extra added, so that's good enough for me.
I don't want to drag the OP's thread off course with a minor dispute, but please note the word highlighted in bold above. The OP's clear intention was to refer to the specific problem which was actually attached in his second post!

You correctly pointed out that textbooks often gloss over the fact that we can only write tan x = sin x / cos x when tan x is defined, but you weren't correcting any of the previous posters because they explained that we needed cos x not equal to zero for the division to be valid, and this condition is precisely the same as saying 'tan x is defined'

Hopefully the OP has enough from all of us to have a better understanding of why the process was correct for the specific problem he attached. It's better to see students asking about this than blindly assuming we can divide by things all the time, which is the more common error!

EDIT: beaten by Zacken while I was composing my essay

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Updated: October 22, 2015
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