So this is some I partially understand, I'm not sure what I don't and do understand because most of my understanding is based on assumptions... sorry if I sound a little stupid!
The equation $6 \cos x - \sin x = 5 $ needs to be turned into the form $ \Re \cos (x + \alpha) $ then solved for in the interval $ -1/2\pi < x < 1/2\pi $.
I turned it into this: $ \sqrt{37} \cos( x + 0.165) $ then
$ \sqrt{37} \cos( x + 0.165) = 5$
$ \cos( x + 0.165) = \frac{5}{\sqrt{37}}$
$ x + 0.165= \arccos( \frac{5}{\sqrt{37}} )$
$ x = \arccos( \frac{5}{\sqrt{37}} ) - 0.165$
$ x = 0.44$ YAY! but... the answer is 0.44 and -0.771
I'm thinking its asking what other value would of the above equation would end up in 5 also? Correct? How do I do this? Could someone explain what is meant by "solve this equation for that interval", and how does one go about it?
A problem I think might be related that I JUST cannot get my head around is this one:
The angle made by a wasps wings horizontally is given by the equation $ \theta = 0.4 \sin600t $, where t is time is seconds. How many times a second does its wing oscillate?
I tried solving this, honest but I do not know where to begin!