How do you find period, amplitude, and midline of # -6*Cos(0.125piX+0.375pi) +3#?

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Answer 1 · 2018-03-19T03:13:38

As below.

Standard form #y = A cos(Bx - C ) + D#

Given #y = -6 cos (0.125 pix + 0.375pi) + 3#

#Amplitude = |A| = 6#

#"Period" = (2pi) / |B| = (2pi) / (0.125pi) = 16#

#"Phase Shift" = (-C) / B = (-0.375pi) / (0.125pi) = -3#

#"Vertical Shift" = D = 3#

graph{-6 cos(0.125 pi x + 0.375 pi) + 3 [-10, 10, -5, 5]}

#"Midline Value" = ((-6+3) + (6 + 3)) / 2 = 3#