Trigonometric Graphs

Front

What is the definition of a trigonometric function?

Back

A trigonometric function relates the angles of a triangle to the lengths of its sides. The primary trigonometric functions are sine, cosine, and tangent.

Front

What is the period of the sine function?

Back

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

Front

What is the amplitude of a sine wave?

Back

The amplitude is the maximum distance from the midline to the peak (or trough) of the wave, representing half the distance between the maximum and minimum values.

Front

What is the range of the sine function?

Back

The range of the sine function is [-1, 1].

Front

What is the domain of the cosine function?

Back

The domain of the cosine function is (-∞, ∞), meaning it is defined for all real numbers.

Front

How does the graph of y = sin(x) differ from y = sin(2x)?

Back

The graph of y = sin(2x) has a period of π, which is half the period of y = sin(x), resulting in more cycles in the same interval.

Front

What is the definition of the tangent function?

Back

The tangent function is defined as the ratio of the sine to the cosine of an angle: tan(x) = sin(x)/cos(x).

Front

What is the vertical shift in the function y = sin(x) + 2?

Back

The vertical shift is 2 units upward, moving the midline of the sine wave from y=0 to y=2.

Front

What is the effect of a negative sign in front of the sine function, such as in y = -sin(x)?

Back

A negative sign reflects the graph of the sine function across the x-axis.

Front

What is the frequency of a sine wave?

Back

Frequency is the number of cycles the wave completes in a unit interval, calculated as 1/period.