Solve Multiple-Angle Equations...1

[nycmathguy]

Section 5.3

Note: I had a real hard time solving this multiple-angle problem. It is not clear to me at all. If wrong, can you solve it in full providing steps as you along?

 

[MathLover1]

40

2sin(2x)+sqrt(3)=0
sin(2x)=-sqrt(3)/2

general solutions:

2x= 4pi/3+2pi*k =>x= 4pi/6+2pi/2*k=> x=2pi/3+pi*k
2x=5pi/3+2pi*k=>x=5pi/6+pi*k


Degrees:
x=120°+180°*k
x=150°+180°*k

 

[nycmathguy]

40

2sin(2x)+sqrt(3)=0
sin(2x)=-sqrt(3)/2

general solutions:

2x= 4pi/3+2pi*k =>x= 4pi/6+2pi/2*k=> x=2pi/3+pi*k
2x=5pi/3+2pi*k=>x=5pi/6+pi*k


Degrees:
x=120°+180°*k
x=150°+180°*k

I almost got it right. Why do we add pi•k and not 2pi•k? Is not sine periodic with 2pi?

 

[MathLover1]

you got 2pi/2•k and simplified is pi•k

 

[nycmathguy]

you got 2pi/2•k and simplified is pi•k

Silly errors on my part.