find principal and symmetry solutions set them equal to each

find principal and symmetry solutions.

set them equal to each other like the first one

2sin(x-1)=-1

f(x) = 10 cos (2x + 1) 5, g(x) = 1.

f(x) = sin (2x 1), g(x) = 1 4 .

(a)2sin(x-1)= -1

=> sin(x-1)= -1/2 => sin(1-x)=1/2=sin(pi/6) => 1-x=pi/6 => x=1-(pi/6)=0.4764 (principal solution)

Symmetry solution 1-x=2npi+pi/6 => x= -2npi+1-pi/6

(b)10 cos (2x + 1) 5 = 1. => 10 cos (2x + 1)=4 =>cos (2x + 1)=4/10=2/5

=> 2x+1=arccos(2/5)=1.16 =>x=(1.16-1)/2=0.08(principal solution)

Symmetry solution 2x+1=2npi+1.16 => x= (2npi+0.16)/2=npi+0.08

(c)sin (2x 1)= 1/ 4 => 2x-1=arcsin(1/4)=0.2526

=>x=1.2526/2=0.6263 ((principal solution)

Symmetry solution 2x-1=2npi+0.2526 => x= (2npi+1.2526)/2=npi+0.6263