Write an equation for the function that is described by the given characteristics.
A sine curve with a period of 4π,an amplitude of 4,a left phase shift of $\frac { \pi } { 4 }$ ,and a vertical translation down 5 units.

A) $y = 4 \sin \left( x + \frac { \pi } { 8 } \right) - 5$
B) $$y = 4 \sin \left( \frac { x } { 2 } + \frac { \pi } { 8 } \right) + 5$$
C) $$y = 4 \sin \left( \frac { x } { 2 } + \frac { \pi } { 8 } \right) - 5$$
D) $y = 4 \sin \left( \frac { x } { 2 } + \pi \right) - 5$
E) $y = 5 \sin \left( \frac { x } { 2 } + \frac { \pi } { 8 } \right) - 4$

Question

Write an equation for the function that is described by the given characteristics. ​
A sine curve with a period of 4π,an amplitude of 4,a left phase shift of $\frac { \pi } { 4 }$ ,and a vertical translation down 5 units.
​
A) $y = 4 \sin \left( x + \frac { \pi } { 8 } \right) - 5$
B) $$y = 4 \sin \left( \frac { x } { 2 } + \frac { \pi } { 8 } \right) + 5$$
C) $$y = 4 \sin \left( \frac { x } { 2 } + \frac { \pi } { 8 } \right) - 5$$
D) $y = 4 \sin \left( \frac { x } { 2 } + \pi \right) - 5$
E) $y = 5 \sin \left( \frac { x } { 2 } + \frac { \pi } { 8 } \right) - 4$

Quizplus · Accepted Answer

The general equation for a sine function is:
y = A sin(B(x-C)) + D 
where 
A = amplitude
B = 2π/period
C = horizontal (or phase) shift
D = vertical shift

In this case, we are given:

- Period = 4π, so B = 2π/(4π) = 1/2
- Amplitude = 4, so A = 4
- Left phase shift = 11, so C = 11
- Vertical translation down 5 units, so D = -5

Putting all of these values into the equation, we get:

y = 4sin(1/2(x - 11)) - 5

which matches choice C.

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