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#1 2013-05-25 22:53:09

atuturay
Member
Registered: 2013-05-25
Posts: 1

Roots of an Equation

Hiii,

I don't know how to work out the root of the equation sinx= 1+cosx for 0°<x<180°

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#2 2013-05-25 23:16:20

zetafunc.
Guest

Re: Roots of an Equation

Squaring both sides might help.

#3 2013-05-25 23:40:11

{7/3}
Member
Registered: 2013-02-11
Posts: 210

Re: Roots of an Equation

Bring cos x to left side and squre.


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#4 2013-05-26 00:18:10

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,259

Re: Roots of an Equation

hi atuturay

Welcome to the forum.

Squaring will give the solutions.  It may also generate values that don't fit the original because (-z)^2 = z^2

An alternative starts like this:

Solve this firstly for x plus alpha and hence get x.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#5 2013-05-26 00:23:27

zetafunc.
Guest

Re: Roots of an Equation

Letting x = arccos(u) or arcsin(u) is another way, although the method is mostly the same as in posts #2 and #3.

#6 2013-05-26 01:31:22

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,860

Re: Roots of an Equation

Won't squaring introduce extraneous solutions?


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#7 2013-05-26 01:54:59

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,259

Re: Roots of an Equation

Won't squaring introduce extraneous solutions?

In post 4 I wrote:

Squaring will give the solutions.  It may also generate values that don't fit the original because (-z)^2 = z^2

But, in this example, as we only want 0 < x < 180, the single, correct solution may be found by squaring.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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