Sin and Cos Graphs period and amp

Front

What is the amplitude of a sine or cosine function?

Back

The amplitude is the maximum distance from the midline of the graph to its peak or trough. It is always a positive value.

Front

What is the period of a sine or cosine function?

Back

The period is the distance along the x-axis for one complete cycle of the wave. For the function f(x) = sin(kx) or f(x) = cos(kx), the period is given by 2π/k.

Front

How do you determine if a function is sine or cosine based on its equation?

Back

If the function has a sine term (e.g., sin(x)), it is a sine function. If it has a cosine term (e.g., cos(x)), it is a cosine function.

Front

What is the effect of the coefficient in front of the sine or cosine function?

Back

The coefficient affects the amplitude of the function. For example, in f(x) = A sin(x), A is the amplitude.

Front

What is the range of a sine function?

Back

The range of a sine function is [-1, 1]. This means the output values will always fall within this interval.

Front

What is the range of a cosine function?

Back

The range of a cosine function is also [-1, 1]. Like sine, the output values will always be within this interval.

Front

What happens to the graph of a sine function when the coefficient of x is increased?

Back

Increasing the coefficient of x (e.g., f(x) = sin(kx)) decreases the period of the function, making it oscillate more frequently.

Front

What happens to the graph of a cosine function when the coefficient of x is increased?

Back

Similar to sine, increasing the coefficient of x in a cosine function decreases its period, resulting in more oscillations.

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 f(x) = A sin(k(x - c)) or f(x) = A cos(k(x - c)).

Front

How do you find the amplitude of the function f(x) = 3 sin(x)?

Back

The amplitude is the absolute value of the coefficient in front of the sine function. Here, the amplitude is |3| = 3.