easy angle thing

**furor celtica** · January 25th 2011, 08:43 PM

ok so i have this list of questions like this one:
find the least positive value of B for which sin(A-B)=cos(A+B)

using translation, odd, periodic properties, etc.
the problem is i totally forgot how to work these out! i know there is a simple method to work this out without staring continually at the sin and cos graphs, i just need a little reminder. thanks

**Sudharaka** · January 26th 2011, 01:10 AM

Originally Posted by furor celtica

ok so i have this list of questions like this one:
find the least positive value of B for which sin(A-B)=cos(A+B)

using translation, odd, periodic properties, etc.
the problem is i totally forgot how to work these out! i know there is a simple method to work this out without staring continually at the sin and cos graphs, i just need a little reminder. thanks

Dear furor celtica,

$\sin(A-B)=\cos(A+B)$

$\cos\left(\frac{\pi}{2}-(A-B)\right)=\cos(A+B)$

$\frac{\pi}{2}-(A-B)=2n\pi\pm(A+B)\mbox{ where }n\in Z$

$A=\frac{\pi}{4}-n\pi\mbox{ or }B=n\pi-\frac{\pi}{4}\mbox{ where }n\in Z$

Therefore the smallest positive value for B would be,

$n=1\Rightarrow{B=\pi-\dfrac{\pi}{4}=\dfrac{3\pi}{4}}$

Hope you understood.

**furor celtica** · January 26th 2011, 03:56 AM

umm i got most of it but at the level i'm at the n is not really appropriate, could you kinda simplify that?

**Sudharaka** · January 26th 2011, 04:47 AM

Originally Posted by furor celtica

umm i got most of it but at the level i'm at the n is not really appropriate, could you kinda simplify that?

Dear furor celtica,

Do you mean that you do not understand how we got the n into the equation?

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