Trig General Solution

[GrandMaster87]

1. The problem statement, all variables and given/known data
Solve for x using general solution
sin2x = 0.5



2. Relevant equations
sin2x= 2sinxcosx


3. The attempt at a solution
arcsin0.5 = 2x
2x = 30 degrees + k360
x = 15 degrees + k180.

Or

2x = (180-30) + k360
2x = 150 + k360
x = 75 + k180

[Elucidus]

1. The problem statement, all variables and given/known data
Solve for x using general solution
sin2x = 0.5



2. Relevant equations
sin2x= 2sinxcosx


3. The attempt at a solution
arcsin0.5 = 2x
2x = 30 degrees + k360
x = 15 degrees + k180.

Or

2x = (180-30) + k360
2x = 150 + k360
x = 75 + k180

Using the arcsine is dangerous since you miss solutions in the second quadrant.

sin2x = 1/2 ==> 2x = 30º + k360º or 150º + k360º

Continue from there.

--Elucidus

[njama]

2x=arcsin(0.5)+2kп

2x=п-arcsin(0.5) +2kп