How do you find the amplitude, period and phase shift for #y=cos3(theta-45^circ)+1/2#?

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Answer 1 · 2018-07-17T12:04:47

As below.

Standard cosine function is #y = A cos (Bx - C) + D#

Given #y = cos (3 theta - 135^@) + 1/2#

#A = 1, B = 3, C = 135^@ = (3pi)/4, D = 1/2#

Amplitude # = |A| = 1#

Period #= (2pi)/|B| = (2 pi) / 3#

Phase Shift #= -C / B = -((3pi)/4) / 3 = -pi/4#, #color(red)(pi/4)# to the LEFT.

Vertical Shift #= D = 1/2#