For with where , find in terms of .
I am terrible at maths so please show any simple easy to understand working out so that I can understand better.
Any help would be appreciated!
Recall the following "transition formula" for going from cosine to sine, where is arbitrary:
Since the numbers and are different by , and since sine is periodic with period , we have also that
whence
Since , we have that lies in the interval
Since you want to solve for , we have by the transition formula above that we might just as well solve
for , where the last equality follows from sine being an odd function.
Since , we have that lies in the interval . Hence both and are numbers in the interval , on which sine is injective, so in solving
for , we can apply to both sides to obtain
or