Write the equation of a sine function that has the following characteristics.

Question

Write the equation of a sine function that has the following characteristics.

Amplitude: 8Amplitude: 8    

Period: piPeriod: π    

Phase shift: one halfPhase shift: 12

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Part 1

Type the appropriate values to complete the sine function.

y equals 8 sine left parenthesis 2 x minus nothing right parenthesisy=88sin22x−enter your response here  

​(Use integers or fractions for any numbers in the expression. Simplify your​ answers.)

Answer 1

y = 8sin(2x +12)

y = Asin(Bx + C) + D

A = (max -min)/2 = 8

C = horizontal shift = 12

D = average = midline = (max+min)/2 = 0 = vertical shift, max = -min

-min-min)/2 = 8, -2min/2 = 8, -min= 8, min = -8, max = 8

B = 2pi/pi = 2 = frequency = inverse of period

Answer 2

y = Asin(Bx + C)

Amplitude = A = 8

Period = 2π/B = π. So, B = 2.

Phase shift = -C/B = 1/2. So, C = -1.

y = 8sin(2x - 1)