Question

The graph of a sinusoidal function intersects its midline at (0,5) and then has a maximum point at (\pi,6)

Write the formula of the function, where x is entered in radians.

f(x)=

Answer 1

f(x)=1sin(1/2x)+5

Explanation:

Answer 2

First, let's use the given information to determine the function's amplitude, midline, and period.

Then, we should determine whether to use a sine or a cosine function, based on the point where x=0.

Finally, we should determine the parameters of the function's formula by considering all the above.

Determining the amplitude, midline, and period

The midline intersection is at y=5 so this is the midline.

The maximum point is 1 unit above the midline, so the amplitude is 1.

The maximum point is π units to the right of the midline intersection, so the period is 4 * π.

Determining the type of function to use

Since the graph intersects its midline at x=0, we should use thesine function and not the cosine function.

This means there's no horizontal shift, so the function is of the form -

a sin(bx)+d

Since the midline intersection at x=0 is followed by a maximumpoint, we know that a > 0.

The amplitude is 1, so |a| = 1. Since a >0 we can conclude that a=1.

The midline is y=5, so d=5.

The period is 4π so b = 2π / 4π = 1/2 simplified.


`f(x) = 1 sin ( (1)/(2)x)+5` = Solution