Identifying Sin Graphs

Front

What is the sine function?

Back

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

Front

What is the range of the sine function?

Back

The range of the sine function is from -1 to 1.

Front

What is the period of the sine function?

Back

The period of the sine function is 2π, meaning it repeats every 2π radians.

Front

How does the sine graph look like?

Back

The sine graph is a smooth, continuous wave that oscillates between -1 and 1, starting at (0,0) and moving up to (π/2, 1), down to (π, 0), down to (3π/2, -1), and back to (2π, 0).

Front

What is the amplitude of the sine function?

Back

The amplitude of the sine function is the maximum distance from the midline to the peak, which is 1 for the standard sine function.

Front

What is the midline of the sine graph?

Back

The midline of the sine graph is the horizontal line that runs through the middle of the wave, which is y=0 for the standard sine function.

Front

What transformations can be applied to the sine graph?

Back

Transformations include vertical shifts, horizontal shifts, reflections, and changes in amplitude and period.

Front

What is the effect of a vertical shift on the sine graph?

Back

A vertical shift moves the entire graph up or down without changing its shape.

Front

What is the effect of a horizontal shift on the sine graph?

Back

A horizontal shift moves the graph left or right, affecting the starting point of the wave.

Front

How do you identify the sine graph from a set of graphs?

Back

Look for a smooth, continuous wave that oscillates between -1 and 1, with a period of 2π.