If the question is express 4 cos x - 3 sin x in the form R
cos(x + α)]
everyone knows that R = 5
but regarding the alpha(&)
tan & = B/A = -3/4 = -36.9
R forumla is 5cos (x + (-36.9))
What i was tot is that if it is cos, the sign in the (x -&)
is opposite that of the orginal function. So if it is "4
cos x - 3 sin x in
the form R cos(x
+
α)" teh sign inside would be +. This is opposite for sin. For sin,
the sign follows. if it is + you write x+&
But firstly, ans is x+36.9
also, is my method correct?
because that is the short cut.
I don't advocate short cuts and pure memorizing of formulas like
that (same for physics) because of instances like this... could
easily make you blur... stupid O levels
R cos(x + α) = R cos x cos α - R sin x sin α
So, comparing coefficients,
R cos α = 4 ---(1)
R sin α = 3 --- (2)
(1)² + (2)² = R² (cos² α+ sin² α) = R² ===> that's why
you get R
(2) / (1) = tan α
tan α = 3/4
And hence you get positive 36.9