Trigonometric and Polar Functions

It becomes four times smaller.

It remains unchanged.

It is doubled.

It is halved.

Alters amplitude cosine wave depending magnitude C.

Shifts graph vertically direction depending on sign D.

Causes reflection across either axis based positivity/negativity variable A.

Shifts graph horizontally direction depending on sign C.

A negative vertical stretch factor

A positive phase shift

A height offset greater than or equal to its radius

A negative amplitude value

$y=-5-\sin(x)$

$y=\cos(2x)+5$

$y=5\tan(x)$

$y=5+\sin(x)$

Subtracting $\pi$ from $x$ to get $y=\cos(x-\pi)$

Multiplying by $-1$ to get $y=-\cos(x)$

Multiplying by $i$ to get $y=i\cos(x)$

Adding $\pi$ to $x$ to get $y=\cos(x+\pi)$

Produces a fractal-like pattern repeating the original waveform within each interval $[n, n+1]$ for all integers $n$

Leads to unpredictable disruptions regarding continuousness disruptively breaking down the classical wave nature

Changing into fractional parts provokes an alteration towards fundamental starting points, hence adjusting initial phases consistently throughout the entire domain

Alteration leads solely towards varying amplitudes maintaining exact periodicity state among consecutive cycles

The number of hours in a day with no sunlight

The average daylight hours over one period

The amplitude or variation in daylight hours

The period or frequency of daylight hour changes through seasons

It has been horizontally stretched.

It has been compressed vertically.

It has been reflected across x-axis.

Its amplitude has increased.

$\frac{\pi}{4}$

2

1

3

$y = \sin(x - 2)$

$y = \sin(x) + 2$

$y = \sin(2 \times x)$

$y = \sin(2x)$