general solution

[jashaan]

for 2sin(x+pi/3)=-1 the general solution i get is, 5pi/6 + 2npi AND 3pi/2 + 2npi

but the book (cambridge) has this weird answer (in attachment) i am not sure how they solved it?? Why is there -pi/2?

[Sine]

for 2sin(x+pi/3)=-1 the general solution i get is, 5pi/6 + 2npi AND 3pi/2 + 2npi

but the book (cambridge) has this weird answer (in attachment) i am not sure how they solved it?? Why is there -pi/2?

3pi/2 + 2npi  and 2npi - pi/2 are both equivalent.

Just look at where 3pi/2 and -pi/2 are on the unit circle. They are both in the exact same position - at the 6 o'clock mark.  The 3pi/2 is just 270 degrees anticlockwise and -pi/2 is 90 degrees rotation clockwise.

[jashaan]

3pi/2 + 2npi  and 2npi - pi/2 are both equivalent.

Just look at where 3pi/2 and -pi/2 are on the unit circle. They are both in the exact same position - at the 6 o'clock mark.  The 3pi/2 is just 270 degrees anticlockwise and -pi/2 is 90 degrees rotation clockwise.

Oh right! So that's just an alternative? But would both my general solutions be correct anyway?

[Sine]

Oh right! So that's just an alternative? But would both my general solutions be correct anyway?

Yeah just a different way of expressing the same solution. The only difference for the two solutions would be the value of n required to produce the same answer.

Your general solutions should be fine.