Question

On the Problem Set 1: Question 1A - 6 b)
How did they get there ? Here's the link :
- Problem: http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/part-a-definition-and-basic-rules/problem-set-1/MIT18_01SC_pset1prb.pdf
- Solution: http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/part-a-definition-and-basic-rules/problem-set-1/MIT18_01SC_pset1sol.pdf

Answer 1

the question was to write sin(x) - cos(x) in terms of Asin (x + c)

answer:
\[\sin (-\Pi / 2) = -1 / \sqrt{2}\]
\[\cos (-\Pi/4) = 1 / \sqrt{2} \]
sin (x) - cos (x) = \[\sqrt{2} * \sin(x) * \cos(-\Pi / 4) + \sqrt{2} * \cos(x) * \sin(-\Pi / 4)\]
This is in the form Sin (a + b) = sin (a) cos (b) + cos (a) sin (b)
\[b = - \Pi / 4\]
\[\sin(x) - \cos(x) = \sqrt{2} (\sin ( x - \Pi /4))\]

Answer 2

This is very clever.

I think you mean \[\sin (-{\pi \over 4}) =-{ 1 \over \sqrt 2}\] in the very top line?

Answer 3

you are right... an over sight on my part... but the general logic remains the same