50 points, explain your answer!

determine the function whose graph is given by (sine graph):

determine the function whose graph is given by (cosine graph):

12.  y = 2 sin(4x) + 1

Step-by-step explanation:

The general form of a sin equation is: y = A sin (Bx - C) + D

D = max - A

   = 3 - 2

   = 1

There is no phase shift so C = 0

A = 2, B = 4, C = 0, D = 1  -->  Equation of the graph is: y = 2 sin (4x) + 1

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12.  

Step-by-step explanation:

The general form of a cos equation is: y = A cos (Bx - C) + D

There is no phase shift so C = 0

A = , B = , C = 0, D = 0  -->  Equation of the graph is:

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)