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**Mann****Guest**

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

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

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

Why did the vector cross the road?

It wanted to be normal.

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**Zz****Guest**

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?

**Zz****Guest**

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

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

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

(approximately) radians approximately

Character is who you are when no one is looking.

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**Zz****Guest**

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

**Zz****Guest**

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?

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

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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**Zz****Guest**

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?

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

The first answer is sufficient.

x=53.13 + 180n degrees

includes 53.13 + 360n degrees!

Character is who you are when no one is looking.

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

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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