TE Sin and Cos Graphs

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 amplitude of a sine or cosine function?

Back

The amplitude is the maximum value of the function from its midline. For example, in y = A sin(x) or y = A cos(x), the amplitude is |A|.

Front

What is the period of the sine and cosine functions?

Back

The period is the distance along the x-axis for the function to complete one full cycle. For y = sin(kx) or y = cos(kx), the period is 2π/|k|.

Front

How do you determine if a function is sine or cosine from its graph?

Back

If the graph starts at the midline and goes up, it is a sine function. If it starts at a maximum or minimum, it is a cosine function.

Front

What is the phase shift in trigonometric functions?

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

Front

What is the vertical shift in sine and cosine functions?

Back

The vertical shift moves the graph up or down. It is determined by the value of 'd' in y = A sin(kx) + d or y = A cos(kx) + d.

Front

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

Back

Changing the coefficient (A) affects the amplitude of the graph. A larger |A| results in a taller graph, while a smaller |A| results in a shorter graph.

Front

What does the graph of y = sin(2x) look like?

Back

The graph of y = sin(2x) has a period of π, meaning it completes one cycle in the interval [0, π].

Front

What does the graph of y = cos(x - π/2) represent?

Back

The graph of y = cos(x - π/2) is a cosine function shifted to the right by π/2 units.