Question

Problem set 1 : 1A-6.
Express in the form Asin (x+c):
sin x + sqroot(3).cos x
I watched the solution it's 2sin (x + pi/3).

Can someone give me some insight in the process to reach the answer ? Also through all the questions I've been through in the problem set none of them were really discussed in the lectures I watched previous to that. Is the goal of the problem Set for us to furnish additional work ?

Answer 1

I'll be more specific with my second question: The lectures thus far in 18.01 have been about the subjects: what is a derivative, how to find derivatives.
The first page of the problem set has questions like : what's the inverse of the function f(x), is f(x) even or odd. That hasn't been discussed in the lectures. So I'm guessing those questions are put so we can check if we have the prerequisite ? And if we don't we have to furnish additional work to answer those questions.
IMO, there should have been some documentations on those subjects before the test, but that's another story.

Answer 2

Ok i got it, divide everything by cos x = tan x + sqroot(3) etc.