- #1
physior
- 182
- 1
hello!
I would like to know how to solve asinx + bcosx = c, with a, b, c being any real numbers (constants)
First, are there any limitations for the above to be valid?
Second, I was introduced to a solution but I cannot fully understand the procedure.
Let's say we have asinx + bcosx = c
We can solve this by using:
R= root of a^2 plus b^2
and
asinx + bcosx = Rsin(x+w)
and
tan(w)=b over a
the first question is, do the above are valid for a, b being either positive or negative?
Second, when we find the "w" using the calculator (by inversing its tan), how do we find which exactly value of w we must use?
Third, when we inverse the sin(x+w), by the calculator, how do we find which exactly values of x+w we must use?
Thanks!
I would like to know how to solve asinx + bcosx = c, with a, b, c being any real numbers (constants)
First, are there any limitations for the above to be valid?
Second, I was introduced to a solution but I cannot fully understand the procedure.
Let's say we have asinx + bcosx = c
We can solve this by using:
R= root of a^2 plus b^2
and
asinx + bcosx = Rsin(x+w)
and
tan(w)=b over a
the first question is, do the above are valid for a, b being either positive or negative?
Second, when we find the "w" using the calculator (by inversing its tan), how do we find which exactly value of w we must use?
Third, when we inverse the sin(x+w), by the calculator, how do we find which exactly values of x+w we must use?
Thanks!