Solve Multiple-Angle Equations...3

[nycmathguy]

Section 5.3

I need step by step notes for certain questions. Questions 39-46 threw me into a Loop-O-Plane.
For study notes, I would like you to solve 44 and 46 providing steps as you go along. Please, use proper math notation as you sometimes do. This is it for today.

 

[MathLover1]

44

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

general solutions for sin(x/2)=-sqrt(3)/2 are

Radians:
x/2=4pi/3+2pi*n
x/2=5pi/3+2pi*n

solve for x
x=8pi/3+8pi*n
x=10pi/3+4pi*n

Degrees:
x=480° +720°*n
x=600° +720°*n

46

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

general solution for tan(x/2)=-sqrt(3) is:

Radians:
x/2= 2pi/3+pi* n
x= 4pi/3+2pi* n

Degrees:
x=240°+360°*n

 

[nycmathguy]

44

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

general solutions for sin(x/2)=-sqrt(3)/2 are

Radians:
x/2=4pi/3+2pi*n
x/2=5pi/3+2pi*n

solve for x
x=8pi/3+8pi*n
x=10pi/3+4pi*n

Degrees:
x=480° +720°*n
x=600° +720°*n

46

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

general solution for tan(x/2)=-sqrt(3) is:

Radians:
x/2= 2pi/3+pi* n
x= 4pi/3+2pi* n

Degrees:
x=240°+360°*n

Thank you so much. I will do all 4 remaining odd number problems later this morning and show my work here. By the way, this is not the first time I play with trigonometric equations.

Precalculus is a review of a course I took at Lehman College in the Spring 1993 semester. I had trouble with trigonometric equations then just as I do now 28 years later. Did I say 28 years later? Wow! I am really getting old.