Determine the sinusoidal function

Question

A sinusoidal function has a minimum located at

(-1,10), and a maximum located at (3, 22). Determine a possible equation to model this function

using sine as the base function and another possible equation using cosine as the base function.

Answer 1

corrected, thought max point was (3,33), not 3(,22)

y=6sin([pi/4]*(x-1))+16

moved zero crossing point of sin from 0 right to +1

see that =+1=(3-(-1))/2 which is middle point between max and min,

f=2pi/period ,,,,period=8 ,

,,6=12/2,

,,,,16=22-6,,,,16 is midline

check x=-1,y=10,,,,x=3,y=22

also

y=6cos([pi/4]*(x-3))+16

moved maximum of cos from 0 to +3

x=-1,y=10,,,,x=3,y=22