Question

Someone want to check my work for me real quick?

For the functions below, find the amplitude, period, phase shift, and vertical translation of the graph for the sinusoid.
y=-6cos(x+pi/4)-5

I used the equation to help;
F(t)=Af(B(t)-C)+D
A=Amp ; B= 2pi/B (Period) C= Phase Shift ; D=Vertical Shift.
Amplitude is : -6
Period is : 2pi/x (Does this mean there is range/domain restrictions?)
Phase shift: pi/4
Vertical translation: -5, it's negative so it will shift left <----
Type of reflection: Vertical? Or is it meaning negative?
Minimum Value of graph: -11
Max. Value of graph: -1.

Answer 1

@Owlcoffee @ganeshie8

Answer 2

Or, will it be a horizontal reflection since of the -6?

Answer 3

And could the period possibly be 0.5?

Answer 4

I'm in a office computer right now, but I can mention a little about this.
The period (the interval in which the whole function can fit and keeps on repeating after) is calculated by, if we consider the function with form: \(y=Acos(mx+c)+B\) will be calculated by \(P=\frac{ 2 \pi }{ m }\), which in this case it is just one, so therefore the period will be \(2\pi\).

Answer 5

Okay! Thank you. That makes sense. And I am thinking since -6cos, that will result in a horizontal reflection. What about the phase shift @Owlcoffee

Answer 6

The phase shift is the same as pelleting all the points to the left pi/4 which would mean that for any angle you'll be sustracting pi/4 to it.

Answer 7

Okay, so I had that. I was just wrong on my Period, I found out what the reflection was. I think that's all I needed, thank you @Owlcoffee !

Answer 8

No problem!

Answer 9

"Period is : 2pi/x (Does this mean there is range/domain restrictions?)" NO.

Answer 10

@mathmale Oh okay! Thank you. I was just curious. Thank you so much.