# 1 pre calc question ?

A cosine function has a period of 5π/6, an amplitude of 6, and a vertical translation 5 units down. The function is not reflected over the x-axis.

What is the equation for this cosine function?

### 2 Answers

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- Wayne DeguManLv 72 months ago
y = acos(bx) + c....where a => amplitude, 2π/b => period and c => vertical translation.

so, a = 6 and c = -5

Now, 2π/b = 5π/6

i.e. b/2 = 6/5

=> b = 12/5

Hence, y = 6cos(12x/5) - 5

See a sketch below.

:)>

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- alexLv 72 months ago
Rule

y = Acos(bx)+c

--> amplitude = A

Period = 2pi/b

vertical translation = c units

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