General Solution

[Sanguinne]

sin(2x)=-1
2x=sin^-1(-1)

what is the difference between substituting 3pi/4 and -pi/4 into the general solution.  Aren't they both the answer to sin^-1(-1). The reason I ask is because I normally sub 3pi/4 and whilst I was doing checkpoints I noticed that there answer had -pi/4.

my answer: and \

checkpoint answer:

ps: I used two general solutions

[lzxnl]

For sin(2x) = -1, you should only really get the solution 2x = -pi/2 + 2npi
x = -pi/4 + n*pi. One solution.

Now, if I define n = k+1, then x = - pi/4 + n*pi = -pi/4 + (k+1)*pi = -pi/4 + k*pi + pi = 3pi/4 + k*pi
The two forms are equivalent.

[abeybaby]

im kind of unsure what you mean... you might find this helpful (page 9)
Methods sample 2013