Asinusoidal function whose period is π2 , maximum value is 10, and minimum value is −4 has a y-intercept of 10. what is the equation of the function described?

the general equation of the sine curve is ⇒ y = a sin ( nx + α ) + b

where : a is the amplitude

             n = 2π/period

             b = shift in the direction of y
             α°= shift in the direction of x

Given period = π/2 ,

maximum value is 10,

minimum value is −4

a y-intercept of 10.

 a = (maximum - minimum)/2 = (10 - -4)/2 = 7
 n = 2π/period = 2π/(π/2) = 4
 b = maximum - a = 10 - 7 = 3
to find α ⇒ y-intercept = 10

y = 10 at x = 0

substitute in the general function

∴   y = a sin ( nx + α ) + b

∴ 10 = 7 sin ( 4*0 + α ) + 3

∴ sin α = 1 ⇒⇒⇒ α = π/2

So, the equation of the function described is as attached in the figure

 y = 7 sin ( 4x + π/2 ) + 3

For me i think it'll land on blue