- #1

mattmannmf

- 172

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Sin (4/(3x+3)) / Sin (4/3x)= 1

can i cancel out the sin's?

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- Thread starter mattmannmf
- Start date

- #1

mattmannmf

- 172

- 0

Sin (4/(3x+3)) / Sin (4/3x)= 1

can i cancel out the sin's?

- #2

rock.freak667

Homework Helper

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Sin (4/(3x+3)) / Sin (4/3x)= 1

can i cancel out the sin's?

No you can't just randomly cancel it out.

But you can rearrange and say that if sinX=sinY then it implies that X=Y.

- #3

mattmannmf

- 172

- 0

what if i was taking the limit of that equation:

Lim Sin (4/(3x+3)) / Sin (4/3x)

x->inf

Lim Sin (4/(3x+3)) / Sin (4/3x)

x->inf

- #4

rock.freak667

Homework Helper

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I think the lim sinf(x) = sin lim f(x) is valid if I remember correctly.

- #5

Mark44

Mentor

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As long as a isn't 0 you can do this:

Sin (4/(3x+3)) / Sin (4/3x)= 1

can i cancel out the sin's?

[tex]\frac{a\cdot b}{a \cdot c} = \frac{b}{c}[/tex]

Do you notice a significant difference between what I did compared to what you're trying to do?

- #6

Susanne217

- 317

- 0

Sin (4/(3x+3)) / Sin (4/3x)= 1

can i cancel out the sin's?

Isn't this equivalent to

working on it-

Last edited:

- #7

jrlaguna

- 107

- 1

[tex] {\sin(x)\over\sin(y)}=2 [/tex]

If you cancel the sin's you get [tex]x/y=2[/tex], which is wrong. But what about taking the denominator to the other side? Then you can do something clever: if [tex]sin(x)=sin(y)[/tex], then there is a known relation between x and y. Either they're equal or...

- #8

rs1n

- 179

- 2

Sin (4/(3x+3)) / Sin (4/3x)= 1

can i cancel out the sin's?

The letters s-i-n in [itex]\sin(x)[/itex] are not variables. Those three letters together stand for an operation -- namely the operation of computing the sine of x. Similarly, we use the "+" symbol to refer to the operation of adding two values.

"Canceling" is the notion of dividing out by a common nonzero number, or by a common variable that stands for a nonzero number. "sin" is not a variable; it is an operation. Canceling is not a matter of "deleting letters and symbols" that appear in both the numerator and denominator.

- #9

Mark44

Mentor

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Does this mean I can't do this...The letters s-i-n in [itex]\sin(x)[/itex] are not variables. Those three letters together stand for an operation -- namely the operation of computing the sine of x. Similarly, we use the "+" symbol to refer to the operation of adding two values.

"Canceling" is the notion of dividing out by a common nonzero number, or by a common variable that stands for a nonzero number. "sin" is not a variable; it is an operation. Canceling is not a matter of "deleting letters and symbols" that appear in both the numerator and denominator.

[tex]\frac{sin x}{n} = 6[/tex]

?

?

- #10

happyg1

- 308

- 0

I thought that [tex]i=\sqrt{-1}[/tex] I'm confused....:)

- #11

jrlaguna

- 107

- 1

But if you want the limit, still can't cancel the sin's (cancel the sins... what would a priest think?) :P But you can do the obvious thing, try to substitute. You get sin(0)/sin(0) so, 0/0... why don't you try now L'Hôpital?

- #12

Char. Limit

Gold Member

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I'd really like someone to cancel my sins...

- #13

Susanne217

- 317

- 0

But if you want the limit, still can't cancel the sin's (cancel the sins... what would a priest think?) :P But you can do the obvious thing, try to substitute. You get sin(0)/sin(0) so, 0/0... why don't you try now L'Hôpital?

There this Wiki-link here

http://en.wikipedia.org/wiki/L'Hôpital's_rule

which gives some good examples on howto use L'Hospitals rule. Something which is a bit strange is that why is it to become a famous mathematician you have to so strange names? ;)

Only mathematician with a easy name to remember is Niels Henrik Abel and Cauchy.

:D Susanne

- #14

jrlaguna

- 107

- 1

- #15

Char. Limit

Gold Member

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There this Wiki-link here

http://en.wikipedia.org/wiki/L'Hôpital's_rule

which gives some good examples on howto use L'Hospitals rule. Something which is a bit strange is that why is it to become a famous mathematician you have to so strange names? ;)

Only mathematician with a easy name to remember is Niels Henrik Abel and Cauchy.

:D Susanne

I'd also include Euclid, Newton, Leibniz, and Neumann on that list, but in general I think you're right. I still can't remember how to spell Ramananan, and he seems to have done everything he can with numbers.

- #16

Susanne217

- 317

- 0

I'd also include Euclid, Newton, Leibniz, and Neumann on that list, but in general I think you're right. I still can't remember how to spell Ramananan, and he seems to have done everything he can with numbers.

Euclid, Newton off cause... :D If I invent a some theory which actually works one day, then I will change my name to L'Susanniwitz then I will surely be remembered :)

- #17

jrlaguna

- 107

- 1

- #18

Susanne217

- 317

- 0

Yeah you are right.

By the way back to the original problem and by using L'Hospital one runs into one of funny requirements that in order for that old french guys theory to work then the limit as show in the example has to be there. And I surgest to the original poster to test if the limit

[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)}[/tex] exists

- #19

jrlaguna

- 107

- 1

In this case, the limit does exist, the conditions on the theorem are met. Promised. The question poser has to work it out, though. (This is homework help.)

- #20

Susanne217

- 317

- 0

In this case, the limit does exist, the conditions on the theorem are met. Promised. The question poser has to work it out, though. (This is homework help.)

The funny thing is I tested this problem on the equation-solver on old TI-92 and it claims that there are several solutions to the OP problem like the solutions are polynomial...

- #21

jrlaguna

- 107

- 1

- #22

Cyosis

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The funny thing is I tested this problem on the equation-solver on old TI-92 and it claims that there are several solutions to the OP problem like the solutions are polynomial...

Your calculator is correct. Don't forget that if you have an equation of the type sin(x)=sin(y) then x=y+2pi*k is a solution for k an integer.

- #23

Susanne217

- 317

- 0

Your calculator is correct. Don't forget that if you have an equation of the type sin(x)=sin(y) then x=y+2pi*k is a solution for k an integer.

Okay,

I guess even though I have dropped my TI Calculator in the floor, spilled Coca Cola on it, hell it still works :D

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