I need help with turning features of a sinusoidal function into a full equation, please! i've asked this about four times and keep getting ignored :( here are the features:

Amplitude = -5
Period =
Frequency =
Midline = y=-3
Maximum Value = -1
Minimum Value = -5

Problem 1

See the attached image (figure 1)

16pi seems like a typo. I'm going to assume that it's a fraction and it is 1/(6pi)

f = 1/(6pi) = frequency

T = 1/f = 1/(1/(6pi)) = 6pi

Amplitude = 2

a = 2

b = 2pi/T = 2pi/(6pi) = 1/3

Midline: y = 3

d = 3

The function is

y = a*sin(bx-c)+d

y = 2*sin(1/3*x-0)+3

y = 2*sin(x/3)+3

the third one

Period = 4pi

T = 4pi

b = 2pi/T = 2pi/(4pi) = 1/2 = 0.5

Amplitude = 2

a = 2

Midline: y = 3

d = 3

y-intercept: (0,3)

The function is a reflection of its parent function over the x-axis, so 'a' is negative meaning a = -2 instead of a = 2

The function is

y = a*sin(bx-c)+d

y = -2*sin(0.5x-0)+3

y = -2*sin(0.5x)+3

the fourth one

a = 10 which is half of the distance between the highest and lowest points

T = 8 is the period

b = 2pi/T = 2pi/8 = pi/4

c = -pi/2 is the phase shift since its really a cosine graph

d = 0 is the midline

The function is

y = a*sin(bx-c)+d

y = 10*sin((pi/4)*x+(-pi/2))+0

y = 10*sin((pi/4)*x+pi/2)

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Step-by-step explanation:

this is all ik i dont even think this is right im sorry

answer: the resulting cross section is a rectangle. solution: a plane parallel to the base of a triangular prism will intersect a cross section that is the same shape as its bases. so the cross section is a triangle.

step-by-step explanation: