How do you write an equation for a cosine function with an amplitude of 2/3, a period of pi, and a vertical shift of 2 units up?

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Answer 1 · 2018-07-25T11:15:12

Equation is #color(indigo)(y = 2/3 cos(2x) + 2#

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

Amplitude #= |A| = 2/3#

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

#:. B = 2#

Phase Shift #= -C / B = 0#

Hence #C = 0#

Vertical Shift # = D = 2#

Hence the equation is #color(indigo)(y = 2/3 cos(2x) + 2#

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