Question

18.01 Single Variable Calculus Problem Set 1 Question 1A-6b

Answer 1

Hello, could you tell me what you are having trouble with on this problem?

Answer 2

if the problem is to find A and ϕ so that
\[ \sin x - \cos x = A \sin (x + \phi) \]

use this idea
\[a \sin x + b \cos x = \sqrt{a^2+b^2}\left( \frac{a}{\sqrt{a^2+b^2}}\sin x +\frac{b}{\sqrt{a^2+b^2}}\cos x\right)
\]

Answer 3

and this idea

Answer 4

with those definitions
\[ a \sin x + b \cos x = \sqrt{a^2+b^2}\left( \cos(\phi)\sin x +\sin(\phi)\cos x\right) \\=\sqrt{a^2+b^2} \sin(x+\phi)\]