Sine and Cosine 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 has a range of [-1, 1] and a period of 2π.

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 has a range of [-1, 1] and a period of 2π.

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 determine the amplitude of a sine or cosine function?

Back

The amplitude of a sine or cosine function is the absolute value of A in the general form y = A sin(Bx + C) + D or y = A cos(Bx + C) + D. It represents the maximum distance from the midline.

Front

What is the period of the sine and cosine functions?

Back

The period of the sine and cosine functions is calculated as 2π/B, where B is the coefficient of x in the function's equation.

Front

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

Back

The phase shift is determined by the value of C in the general form y = A sin(Bx + C) + D or y = A cos(Bx + C) + D. It represents the horizontal shift of the graph.

Front

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

Back

The vertical shift is determined by the value of D in the general form y = A sin(Bx + C) + D or y = A cos(Bx + C) + D. It represents the upward or downward shift of the graph.

Front

What is the relationship between sine and cosine functions?

Back

Sine and cosine functions are related through the identity sin(x) = cos(π/2 - x). They are phase-shifted versions of each other.

Front

How do you find the x-intercepts of a sine function?

Back

To find the x-intercepts of a sine function, set the function equal to zero and solve for x: A sin(Bx + C) + D = 0.