TE Sin and Cos Graphs

Front

What is the sine function?

Back

The sine function, denoted as sin(x), is a periodic function that describes the y-coordinate of a point on the unit circle as it rotates around the origin. It oscillates between -1 and 1.

Front

What is the cosine function?

Back

The cosine function, denoted as cos(x), is a periodic function that describes the x-coordinate of a point on the unit circle as it rotates around the origin. It oscillates between -1 and 1.

Front

What is the amplitude of a sine or cosine graph?

Back

The amplitude is the maximum distance from the midline (equilibrium position) to the peak (maximum) or trough (minimum) of the graph. It is half the distance between the maximum and minimum values.

Front

What is the period of a sine or cosine function?

Back

The period is the length of one complete cycle of the wave. For the basic sine and cosine functions, the period is 2π.

Front

What does the equation y = A sin(Bx) represent?

Back

In this equation, A represents the amplitude, B affects the period of the function, and x is the variable. The period can be calculated as 2π/B.

Front

What does the equation y = A cos(Bx) represent?

Back

Similar to the sine function, in this equation, A represents the amplitude, B affects the period, and x is the variable. The period is also calculated as 2π/B.

Front

How do you determine the maximum value of a sine or cosine function?

Back

The maximum value of a sine or cosine function is equal to the amplitude (A) when the function is in the form y = A sin(Bx) or y = A cos(Bx).

Front

How do you determine the minimum value of a sine or cosine function?

Back

The minimum value of a sine or cosine function is equal to -A when the function is in the form y = A sin(Bx) or y = A cos(Bx).

Front

What is the phase shift in a sine or cosine function?

Back

The phase shift is the horizontal shift left or right for the graph of the function. It is determined by the value of C in the equations y = A sin(B(x - C)) or y = A cos(B(x - C)).

Front

What is the frequency of a sine or cosine function?

Back

The frequency is the number of cycles that occur in a unit interval. It is the reciprocal of the period, calculated as 1/period.