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#1 2006-04-22 07:01:14

Mann
Guest

I need to know if I did this right!

, I have the equation;  2tanx/2 = 1, which I was supposed to solve, and I got x=180+n*pi. Is this correct?

#2 2006-04-22 08:04:24

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: I need to know if I did this right!

Ooh, I think you've mixed up degrees and radians there.

Let's see what I get, anyway.

2tan(x/2) = 1
tan(x/2) = 1/2
x/2 = tan-¹ (1/2)
x/2 = 0.463... + πn
x = 0.927... + 2πn


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It wanted to be normal.

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#3 2006-04-22 08:12:35

Zz
Guest

Re: I need to know if I did this right!

mathsyperson wrote:

Ooh, I think you've mixed up degrees and radians there.

Let's see what I get, anyway.

2tan(x/2) = 1
tan(x/2) = 1/2
x/2 = tan-¹ (1/2)
x/2 = 0.463... + πn
x = 0.927... + 2πn

I see. I was completely wrong then. I need the answer in degrees, though, so would that be 53 degrees?

#4 2006-04-22 08:13:44

Zz
Guest

Re: I need to know if I did this right!

Zz wrote:

I see. I was completely wrong then. I need the answer in degrees, though, so would that be 53 degrees?

I mean 53 +2pi n

#5 2006-04-22 11:55:40

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,559

Re: I need to know if I did this right!

x = 53.13... + 360n (using degrees)
x = 0.927... + 2πn (using radians)

There may even be a more exact way to express tan-¹ (1/2)


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#6 2006-04-22 17:09:45

ganesh
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Registered: 2005-06-28
Posts: 16,087

Re: I need to know if I did this right!

(approximately)

radians approximately


Character is who you are when no one is looking.

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#7 2006-04-22 19:03:54

Zz
Guest

Re: I need to know if I did this right!

I see, that's great. Thanks a lot guys smile

#8 2006-04-22 19:05:42

Zz
Guest

Re: I need to know if I did this right!

ganesh wrote:

(approximately)

radians approximately

I asked this on another forum though, and they said that I should add 180degrees, so I got 2 answers;

x1=53+360n
x2=(53+180)+360n


What was that all about?

#9 2006-04-22 19:42:12

ganesh
Moderator
Registered: 2005-06-28
Posts: 16,087

Re: I need to know if I did this right!

That is true because

Therefore, theanswer should be
x=53.13 +180(n) degrees
where n=0,1,2,3,4....etc.


Character is who you are when no one is looking.

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#10 2006-04-22 19:49:33

Zz
Guest

Re: I need to know if I did this right!

ganesh wrote:

That is true because

Therefore, theanswer should be
x=53.13 +180(n) degrees
where n=0,1,2,3,4....etc.

So I could write the full answer as;
x=53.13 +180(n) degrees
x2=(53+180)+360(n) degrees


or is the first line sufficient?

#11 2006-04-22 23:30:30

ganesh
Moderator
Registered: 2005-06-28
Posts: 16,087

Re: I need to know if I did this right!

The first answer is sufficient.
x=53.13 + 180n degrees
includes 53.13 + 360n degrees!


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#12 2006-04-23 07:35:10

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: I need to know if I did this right!

Hold on though.

Although tanθ = tan(θ+180), in this case θ = x/2.

Therefore, to get it back to x you need to think of it as tan2θ = tan(2θ+360).

So only solutions of the form 53.13 + 360n work. If you put the others back into the equation, you should get them equalling -4. Which is wrong.


Why did the vector cross the road?
It wanted to be normal.

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