Write an equation for the function that is described by the given characteristics.
A sine curve with a period of $\pi$, an amplitude of 4, a right phase shift of $\frac { \pi } { 2 }$ , and a vertical translation up 7 units.

A)y = 10 + 4 sin (2x + $\pi$)
B)y = 7 + 4 sin (2x - $\pi$)
C) y = 9 - 4 sin (2x + $\pi$)
D)y = 8 + 4 sin (- 2x - $\pi$)
E)y = 11 + 7 sin (2x - $\pi$)

Question

Write an equation for the function that is described by the given characteristics.  
A sine curve with a period of $\pi$, an amplitude of 4, a right phase shift of $\frac { \pi } { 2 }$ , and a vertical translation up 7 units.
 
A)y = 10 + 4 sin (2x + $\pi$)
B)y = 7 + 4 sin (2x - $\pi$)
C) y = 9 - 4 sin (2x + $\pi$)
D)y = 8 + 4 sin (- 2x - $\pi$)
E)y = 11 + 7 sin (2x - $\pi$)

Quizplus · Accepted Answer

The general form of a sine function is $y = A \sin(B(x - C)) + D$, where $A$ is the amplitude, $B$ determines the period by $2\pi/B$, $C$ is the phase shift, and $D$ is the vertical translation. Given an amplitude of 4, a period of $\pi$ (which implies $B = 2$), a phase shift to the right of $\frac{\pi}{2}$ (which translates to $C = \frac{\pi}{2}$), and a vertical translation up 7 units, the equation becomes $y = 7 + 4 \sin(2(x - \frac{\pi}{2}))$. Simplifying the phase shift part gives $y = 7 + 4 \sin(2x - \pi)$, which matches option B.

Write an Equation for the Function That Is Described by the Given