find a, b , and h so that f(x)= a sin (b(x-h))
f(x)=5cosx+2sinx

Question

find a, b , and h so that f(x)= a sin (b(x-h))
f(x)=5cosx+2sinx

mani_jha · Answer

The two given functions are equal.
Break up the first one using:
$$\sin(A-B)=sinAcosB-cosAsinB$$
then compare with the second one.
Got it? Come on, try this. It's a sum worth solving

anonymous · Answer

its confusing i dont understand the procedure

mani_jha · Answer

Ok, Do you know the formula that I have stated above?

anonymous · Answer

yea..sort of

mani_jha · Answer

Ok. Now see the first function:
$$f(x)=a \sin (bx-bh)$$
Do you agree?
Now take A=bx and B=bh
and then use that formula. In this formula, you've got to take sine of first angle, multiply it with cosine of the other, and then add the sine of the other multiplied by the cosine of the first.
So, this becomes:
$$f(x)=a(\sin bx \cos bh-\cos bx \sin bh)$$
Is it clear so far?