The graph depicts a function in the form y c cosx y c si

The graph depicts a function in the form y = c + cos(x), y = c + sin(x), y = cos(x - d). or y = sin(x - d) where d is the least possible positive value. Determine the equation. y = cos(pi/3)

Solution

maximum value=1

minimum value=-1

amplitude =|a| =(1-(-1))_/2

amplitude =|a| =1

period =2_/b =((5_/3)-(-_/3))

=>2_/b =2

=>b=1

phase shift =d_/b =(2_/3)-(_/2)

=>d_/1 =_/6

=>d =_/6

so the equation is y =cos(x-(_/6))