Write an equation of the sine function with:

amplitude = 7
period = 3π
phase shift = π
vertical shift = -7

Question

Write an equation of the sine function with:

amplitude = 7
period = 3π
phase shift = π
vertical shift = -7

anonymous · Answer

So lets think about what these things mean... Are you familiar with amplitude?

anonymous · Answer

not really :(

anonymous · Answer

OK, Amplitude is how much to 'amplify' the function by.

anonymous · Answer

or you could say, multiply.

anonymous · Answer

If you have 5Sin(x) then its amplitude is 5 (the wave will hit a maximum of 5 and a minimum of -5.

anonymous · Answer

ok got it

anonymous · Answer

So hopefully that explains amplitude.
The period is the length of a wave before it starts repeating itself. The usual period of a sine function is 2Pi as the wave will begin to repeat after that point in time.
I.e. period of Sin(x) is 2Pi.
Is this making sense so far?

anonymous · Answer

so its 7sinx

anonymous · Answer

yep, thats right, 7 sin x (for the amplitude part)

unklerhaukus · Answer

$$y(x)=A\sin(\omega t+\phi)+b$$

$A$ is the Amplitude

$\omega$ is the angular frequency

$\frac{\omega}{2\pi}=$frequency of oscillation 

$\tau$ is the period and $\tau=\frac{2\pi}{\omega}$

$\phi$ is the phase shift 

$b$ is the vertical shift

anonymous · Answer

You are best of taking a look at http://www.intmath.com/trigonometric-graphs/trigo-graph-intro.php. This will explain it properly.