Posted by **alex** on Sunday, May 22, 2011 at 1:31am.

what are the amplitude and period of the sinusoid y=6cosx+7sinx?

- pre cal -
**Reiny**, Sunday, May 22, 2011 at 8:33am
We could write 6cosx + 7sinx as a single

sine function of the form asin(x + A)

asin(x+A) = asinxcosA + acosxsinA = 7sinx + 6cosx

let x=0

---> asinA = 6 or sinA = 6/a

let x=π/2

---> acosA = 7 or cosA = 7/a

but sin^2 A + cos^2 B = 1

36/a^2 + 49/a^2 = 1

a^2 = 85

a =√85

so the amplitude is √85

and the period is 2π, (A is simply a phase shift)

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