need someone to check my work

[abel muroi]

i was given this problem 2 sin² x + 3 = 4 and was told to find ALL possible solutions

so here is my work...


2 sin² x + 3 = 4
2 sin² x = 1
sin² x = 1/2
sin x = +- 1/(squareroot 2)

so the sin of 1/(squareroot 2) is 45 degrees

the general solution must be x = pi/4 + k*2pi



do i have the correct general solution?

 

[Steven G]

i was given this problem 2 sin² x + 3 = 4 and was told to find ALL possible solutions

so here is my work...


2 sin² x + 3 = 4
2 sin² x = 1
sin² x = 1/2
sin x = +- 1/(squareroot 2)

so the sin of 1/(squareroot 2) is 45 degrees

the general solution must be x = pi/4 + k*2pi



do i have the correct general solution?

No, this is not complete at all. There are 4 solutions to this equation in the domain (!!) [0, 2pi). You only found 1 solution. How about solutions in the other 3 quadrants? Might there be solutions there? Adding on the k*2pi to the solution you found is correct.