Solve Multiple-Angle Equations...2

[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]

42.

sec(4x)-2=0
sec(4x)=2

general solutions for sec(4x)=2 are

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

solve for x
x= pi/12+(pi/2)*k
x= 5pi/12+(pi/2)*k

Degrees:
x=15°+90°*k
x=75°+90°*k

 

[nycmathguy]

42.

sec(4x)-2=0
sec(4x)=2

general solutions for sec(4x)=2 are

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

solve for x
x= pi/12+(pi/2)*k
x= 5pi/12+(pi/2)*k

Degrees:
x=15°+90°*k
x=75°+90°*k

I will do all the odd numbers for this set today.