The y-coordinate of a point on the unit circle corresponding to a given angle.

The x-coordinate of a point on the unit circle corresponding to a given angle.

The interval over which the sine function completes one full cycle, which is $2\pi$.

The interval over which the cosine function completes one full cycle, which is $2\pi$.

The amplitude is the maximum displacement of the function from its midline. For standard sine and cosine, it's 1.

The set of all possible output values of the sine function, which is [-1, 1].

The set of all possible output values of the cosine function, which is [-1, 1].

The points where the graph intersects the x-axis, i.e., where the function value is zero.

A transformation that moves the entire graph up or down by a constant value.

A horizontal shift of the sine or cosine graph, often represented as $sin(x - c)$ or $cos(x - c)$, where 'c' is the phase shift.

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.

The maximum value is $A + D$.

The minimum value is $-|A| + D$.

Period = $\frac{2\pi}{|B|}$

Period = $\frac{2\pi}{|B|}$

Set $\sin(x) = 0$ and solve for x. The solutions are $x = 0, \pi, 2\pi$.

Set $\cos(x) = 0$ and solve for x. The solutions are $x = \frac{\pi}{2}, \frac{3\pi}{2}$.

1. Determine the amplitude (A). 2. Identify key points (0, 0), $(\frac{\pi}{2}, A)$, $(\pi, 0)$, $(\frac{3\pi}{2}, -A)$, $(2\pi, 0)$. 3. Sketch the curve.

1. Determine the amplitude (A). 2. Identify key points (0, A), $(\frac{\pi}{2}, 0)$, $(\pi, -A)$, $(\frac{3\pi}{2}, 0)$, $(2\pi, A)$. 3. Sketch the curve.

The phase shift is 'c'. If c is positive, the shift is to the right; if c is negative, the shift is to the left.

The phase shift is 'c'. If c is positive, the shift is to the right; if c is negative, the shift is to the left.