Question

Multiple choice - What sine function represents an amplitude of 4, a period of pi/2, no horizontal shift, and a vertical shift of −3?

Answer 1

a)f(x) = -3 sin 4x +4
b) f(x)= 4 sin 4x -3
c) f(x) = 4 sin (pi/2) x -3
d) f(x) = -3 sin (pi/2) x + 4

Answer 2

For the function \[\large a ~sin (bx-c)+d\] \[\large amplitude= \left| a \right|\]\[\large period=\frac{2\pi}{b}\]\[\large vertical ~shift = d\]

Answer 3

I'm not exactly sure how to plug in the inside of the parentheses. So far I have \[\left| 4 \right| \sin (???) - 3\] @LegendarySadist

Answer 4

You can disregard the c in this example, as it's used for the phase shift, aka horizontal shift. So the b will be the integer before the \(x\)

Answer 5

I knew that c was the horizontal shift, but what exactly is b?

Answer 6

b is just the number before the x. For option #2, b is 4 and for option #3 b is \(\large \frac{\pi}{2}\)

Answer 7

I can see that b is before x, but I don't understand what I should plug in for b, or how to figure that out.

Answer 8

So we are looking for b, and we know the period. We'd set it up like this. \[\large \frac{2\pi}{b}=\frac{\pi}{2}\] Now cross multiply and solve for b

Answer 9

so b = 2?

Answer 10

\[\large \frac{2\pi}{2} = \frac{\pi}{2}\\\large \pi = \frac{\pi}{2}?\] No b is not 2

Answer 11

Herp, I forgot to multiply 2pi by pi!

Answer 12

\[\large \frac{2\pi}{b} = \frac{\pi}{2}\] Cross multiplying will get you \[\large 4\pi=\pi b\]

Answer 13

Can't you then just cancel out the pi's and get 4 = b?

Answer 14

Yep, that would be it. Good job :)

Answer 15

Thank you very much!

Answer 16

\[\huge \color{aqua}N\color{fuchsia}o \space \color{lime}P \color{orange}r \color{blue}o \color{maroon}b \color{red}l \color{olive}e \color{purple}m \ddot\smile \]

Answer 17

c: