How do you find the amplitude and period of a function #y = -½ cos(π/3) x#?

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Answer 1 · 2018-08-05T11:19:55

#color(brown)("Amplitude " = 1/2, "Period " = 6#

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

#y = -1/2 cos(pi/3 x)#

#A = -1/2, B = pi/3, C = D = 0#

#Amplitude = |A| = |-1/2| = 1/2#

#"Period " = (2pi) / |B| = (2pi) / (pi/3) = 6#

"Phase Shift " = -C / B = 0#

#"Vertical Shift ' = D = 0#

graph{-1/2 cos(pi/3 x) [-10, 10, -5, 5]}