Solving Difficult Wave Function Problems

[blaster]

i am having difficulty with the wave function.
for example in the exercise we are told to write the expression :

a cos x+ b sin x in the form k cos(x-a)

This i had little problem with and was able to work out what quadrant i shoul use etc what i mean is the

all positive. sin positive, tan positive and cosine positive qudarants

but the next exercise was expressing

a cos x + b sin x in other forms such as:

k cos(x+a) k sin(x-a) and k(sin x+a)

with these i am able to work out the k. however when it comes down to the quadrat i do not no whether to take away 180 add 180 or take away 360 if you know what i mean.

 

[blaster]

Why no help?

Have I not been clear enough? Why am I not getting any help? Any questions?

 

[dextercioby]

a=A\cos\alpha

b=A\sin\alpha

Therefore

a\cos x+b\sin x=A\cos(x-\alpha)

Daniel.

 

[Hurkyl]

If you've already written it in the form k cos (x-a), then you can get the others simply by doing simple arithmetic, or applying basic facts about the trig functions...

Or, isn't it possible to do the same type of work to arrive at that form from scratch? ...

 

[shaner-baner]

try using a trig identity to go backwards, i.e. write k*sin(x-a) as a sum or difference of sines and cosines. then equate the coefficients to derive expressions for k and a.