write a sine function

Question

Write a sine function that has an amplitude of 3, a midline of 5 and a period of 7π​/3

Answer 1

Hello Marcela,

Any sine function has this general equation: y = A sin (Bx + C) + D where:

A = amplitude

B = 2pi/Period

C = phase shift

D = midline

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You're told the sine function has:

1. an amplitude of 3 so A = 3
2. a midline of 5 so D = 5
3. a period of 7π/3 so B = 2π/(7π/3) = 2π * 3/7π = 6π/7π = 6/7
4. no mention of phase shift so C = 0

Putting it all together, your sine function will be y = 3 sin (6x/7) + 5

Answer 2

y = 2Sin[(6/7)]x + 5

In general, y = aSinb(x-c) + d

a = amplitude = 2

b = 2pi/period = [2pi/(7pi/3)] = 6/7

c = phase shift = 0

d = vertical shift = 5

Note that the high will be 8 and the low will be 2.