Key Features of Sine and Cosine

Front

What is the sine function?

Back

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

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 half the distance between the maximum and minimum values of the function.

Front

How do you find the period of a sine or cosine function?

Back

The period of a sine or cosine function can be found using the formula: Period = 2π/B, where B is the coefficient of x in the function.

Front

What does the vertical shift in the function y=a*sin(bx - c)+d represent?

Back

The vertical shift is represented by the value d, which moves the graph up or down on the y-axis.

Front

What is the maximum value of y = 3 cos 2x?

Back

The maximum value is 3, which is the amplitude of the function.

Front

What is the minimum value of y = -2 sin x?

Back

The minimum value is -2, which is the negative amplitude of the function.

Front

What is the relationship between sine and cosine functions?

Back

Sine and cosine functions are phase-shifted versions of each other. Specifically, sin(x) = cos(x - π/2) and cos(x) = sin(x + π/2).

Front

What is the frequency of a sine or cosine function?

Back

Frequency is the number of cycles the function completes in a unit interval. It is calculated as Frequency = 1/Period.

Front

What is the effect of changing the value of B in y = a*sin(bx)?

Back

Changing the value of B affects the period of the function. A larger B results in a shorter period, meaning the function oscillates more frequently.