Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

Login

Username

Password

Not registered yet?

#1 2013-05-26 20:53:09

atuturay
Novice

Offline

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°

#2 2013-05-26 21:16:20

zetafunc.
Guest

Re: Roots of an Equation

Squaring both sides might help.

#3 2013-05-26 21:40:11

{7/3}
Full Member

Offline

Re: Roots of an Equation

Bring cos x to left side and squre.


There are 10 kinds of people in the world,people who understand binary and people who don't.

#4 2013-05-26 22:18:10

bob bundy
Moderator

Offline

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

#5 2013-05-26 22:23:27

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 23:31:22

anonimnystefy
Real Member

Offline

Re: Roots of an Equation

Won't squaring introduce extraneous solutions?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#7 2013-05-26 23:54:59

bob bundy
Moderator

Offline

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

Board footer

Powered by FluxBB