Sin and Cos Graphs (identify)

Front

What is the sine function?

Back

The sine function, denoted as sin(x), is a trigonometric function that represents the ratio of the length of the opposite side to the hypotenuse in a right triangle.

Front

What is the cosine function?

Back

The cosine function, denoted as cos(x), is a trigonometric function that represents the ratio of the length of the adjacent side to the hypotenuse in a right triangle.

Front

What is the general form of a sine function?

Back

The general form of a sine function is y = A sin(Bx + C) + D, where A is the amplitude, B affects the period, C is the phase shift, and D is the vertical shift.

Front

What is the general form of a cosine function?

Back

The general form of a cosine function is y = A cos(Bx + C) + D, where A is the amplitude, B affects the period, C is the phase shift, and D is the vertical shift.

Front

How do you identify a sine function from its equation?

Back

A sine function will have 'sin' in its equation, such as y = sin(x) or y = 2sin(2x).

Front

How do you identify a cosine function from its equation?

Back

A cosine function will have 'cos' in its equation, such as y = cos(x) or y = 3cos(x).

Front

What is amplitude in sine and cosine functions?

Back

Amplitude is the maximum distance from the midline of the graph to the peak or trough. It is represented by the coefficient A in the equations.

Front

What is the period of sine and cosine functions?

Back

The period is the distance along the x-axis for one complete cycle of the wave. It is calculated as 2π/B, where B is the coefficient of x.

Front

What is a phase shift in sine and cosine functions?

Back

Phase shift is the horizontal shift left or right for the graph of the function, determined by the value of C in the equations.

Front

What is a vertical shift in sine and cosine functions?

Back

Vertical shift moves the graph up or down, determined by the value of D in the equations.