Curve sketching for trig functions (1 Viewer)

[VenomP]

y = cos (x+pi/4)

This fairly straightforward, the cos curve shifted pi/4 units to the left.

I'm just wondering what happens when you add this to the equation...

y = cos 2(x+pi/4)

Is everything shifted twice as far?

Any help is appreciated.

 

[midifile]

No. It only changes the amplitude (the y-value extent of a graph).

However, if you change y = cos(x) to y = cos (2x), that changes the cycle.

The amplitute is affected by the number in front of the cos, which is 1, so the amplitude is still 1. That 2 affects the period.
The period = 2pi/n = 2pi/2 = pi
and the graph is shifted pi/4 to the left

 

[3unitz]

y = cos (x+pi/4)

This fairly straightforward, the cos curve shifted pi/4 units to the left.

I'm just wondering what happens when you add this to the equation...

y = cos 2(x+pi/4)

Is everything shifted twice as far?

Any help is appreciated.

consider the graph of y = cos x,

it cuts the x axis at pi/2, and dips down to -1 at pi.

if we have y = cos (2x) now,

at x = pi/4, we have y = cos (2 x pi/4) = cos (pi/2) = 0
i.e. it now cuts the x axis at pi/4 instead of pi/2,

infact at pi/2 now, y = cos (2 x pi/2) = cos (pi) = -1 is where our curve dips to -1

in other words its cutting the x-axis twice as much: View attachment 16630

 

[lyounamu]

The amplitute is affected by the number in front of the cos, which is 1, so the amplitude is still 1. That 2 affects the period.
The period = 2pi/n = 2pi/2 = pi
and the graph is shifted pi/4 to the left

Ah, yeah. I somehow thought that the number was in front.

I can see better now.