$\sin(x)$: Starts at (0,0). | $\cos(x)$: Starts at (0,1).

Sine: Odd function, symmetric about the origin. | Cosine: Even function, symmetric about the y-axis.

$\sin(x)$: 0, $\pi$, $2\pi$ | $\cos(x)$: $\frac{\pi}{2}$, $\frac{3\pi}{2}$

$\sin(x)$: Maximum value of 1 at $\frac{\pi}{2}$ | $\cos(x)$: Maximum value of 1 at 0 and $2\pi$

$\sin(x)$: Minimum value of -1 at $\frac{3\pi}{2}$ | $\cos(x)$: Minimum value of -1 at $\pi$

Both shift the graph to the right by the amount of the phase shift. | The overall shape remains the same, just translated.

Both stretch or compress the graph vertically. | A larger amplitude makes the peaks and troughs more extreme.

Both compress or stretch the graph horizontally. | A smaller period means more cycles within the same interval.

Both move the entire graph up or down by the shift amount. | The midline of the graph changes accordingly.

Sine: y-coordinate on the unit circle. | Cosine: x-coordinate on the unit circle.

It indicates the maximum displacement of the graph from its midline, representing the maximum value the function attains.

It represents the length of one complete cycle of the cosine function before the pattern repeats.

By observing the horizontal displacement of the graph compared to the standard sine or cosine function. Where does the cycle BEGIN relative to the origin?

The graph of $-\sin(x)$ is a reflection of the graph of $\sin(x)$ over the x-axis.

The graph of $-\cos(x)$ is a reflection of the graph of $\cos(x)$ over the x-axis.

It indicates that the entire graph has been moved up or down, changing the midline of the function.

Identify the amplitude, period, phase shift, and vertical shift, and then plug these values into the general form of the sine or cosine function.

The steepness relates to how quickly the function's value is changing at that point. Steeper sections indicate more rapid change.

The x-intercepts correspond to the angles on the unit circle where the sine (y-coordinate) or cosine (x-coordinate) is equal to zero.

By examining the period of the graph. A shorter period indicates horizontal compression, while a longer period indicates horizontal stretching.

The y-coordinates of points on the unit circle, as you move counterclockwise around the circle, correspond to the values of the sine function at those angles.

The x-coordinates of points on the unit circle, as you move counterclockwise around the circle, correspond to the values of the cosine function at those angles.

Starts at (0,0), oscillates between -1 and 1, has a period of $2\pi$, and is an odd function (symmetric about the origin).

Starts at (0,1), oscillates between -1 and 1, has a period of $2\pi$, and is an even function (symmetric about the y-axis).

Changing the amplitude stretches or compresses the graph vertically. A larger amplitude means a greater maximum and minimum value.

Changing the period compresses or stretches the graph horizontally. A smaller period means the function oscillates more frequently.

A vertical shift moves the entire graph up or down. Adding a constant 'D' to the function shifts it up by 'D' units.

A phase shift moves the entire graph left or right. It's a horizontal translation determined by the value C/B in the general form.

Because their graphs repeat their pattern over regular intervals (periods).

In a right triangle, sine is the ratio of the opposite side to the hypotenuse, and cosine is the ratio of the adjacent side to the hypotenuse.