<span>the general equation of the sine curve is ⇒ y = a sin ( nx + α ) + b
</span><span>
</span><span>where : a is the amplitude
</span><span>
</span><span> n = 2π/period
</span><span>
</span> b = shift in the direction of y
α°= shift in the direction of x
<span>Given period = π/2 ,
</span><span>
</span><span>maximum value is 10,
</span><span>
</span><span>minimum value is −4
</span><span>
</span><span>a y-intercept of 10.
</span>
a = (maximum - minimum)/2 = (10 - -4)/2 = 7
n = 2π/period = 2π/(π/2) = 4
b = maximum - a = 10 - 7 = 3
to find α <span>⇒ y-intercept = 10
</span><span>
</span><span>y = 10 at x = 0
</span>
<span>substitute in the general function
</span><span>
</span>∴ y <span>= a sin ( nx + α ) + b
</span><span>
</span><span>∴ 10 = 7 sin ( 4*0 + α ) + 3
</span><span>
</span><span>∴ sin α = 1 ⇒⇒⇒ α = π/2</span>
So, <span>
the equation of the function described is as attached in the figure</span><span>
</span><span>
y = 7 sin ( 4x + π/2 ) + 3</span>