Trig General Solution: Solve for x using sin2x = 0.5

[GrandMaster87]

Homework Statement

Solve for x using general solution
sin2x = 0.5

Homework Equations

sin2x= 2sinxcosx

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]

Homework Statement

Solve for x using general solution
sin2x = 0.5

Homework Equations

sin2x= 2sinxcosx

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