Find the values of the amplitude period and phase shift for

Find the values of the amplitude, period, and phase shift for each trigonometric function. For the phase shift, be sure to include direction of the shift:

Solution

y = A sin ( Bx - C) ---------------------------------------1

here A = amplitude

period = 2*pie / B

a) y = 4 cos( x+pie)

by comparing it with eq 1 ( general eq)

A = 4

period = 2*pie / 1 = 2 pie

phase shift, x+ pie = 0

x = - pie to left

B) y = 3*sin ( - ( pie/2)( x-1) ( sin ( -@) = - sin@)

= - 3*sin( ( pie/2)( x-1))

so A = 3

period = 2*pie / ( pie/2)

= 4

phase shift , ( pie/2)*( x-1) = 0

x = 1 to right

C) y = (1/2)*sin ( 1/3)*x + pie)

A = 1/2

period = 2*pie / 1/3

= 6*pie

phase shift , (1/3)*x + pie = 0

x = - 3*pie to left

D) y = - 5*cos ( - ( 4x + 3*pie)) ( cos ( -@) = cos@)

= - 5 cos( 4x+ 3 pie)

A = 5

period = 2*pie /4

= pie /2

phase shift , 4x + 3pie = 0

x = - 3*pie / 4 to left