Identifying Trigonometric Function Graphs

Front

What is the graph of sin(x) characterized by?

Back

The graph of sin(x) is a smooth, continuous wave that oscillates between -1 and 1, with a period of 2π.

Front

What is the graph of cos(x) characterized by?

Back

The graph of cos(x) is similar to sin(x) but starts at its maximum value of 1 when x=0, also oscillating between -1 and 1 with a period of 2π.

Front

What is the graph of tan(x) characterized by?

Back

The graph of tan(x) has vertical asymptotes where cos(x) = 0, oscillates between -∞ and +∞, and has a period of π.

Front

What is the graph of csc(x)?

Back

The graph of csc(x) is the reciprocal of sin(x), with vertical asymptotes where sin(x) = 0, and it oscillates between -∞ and -1, and 1 and +∞.

Front

What is the graph of sec(x)?

Back

The graph of sec(x) is the reciprocal of cos(x), with vertical asymptotes where cos(x) = 0, oscillating between -∞ and -1, and 1 and +∞.

Front

What is the period of sin(x) and cos(x)?

Back

The period of both sin(x) and cos(x) is 2π.

Front

What is the period of tan(x)?

Back

The period of tan(x) is π.

Front

What is the amplitude of sin(x) and cos(x)?

Back

The amplitude of both sin(x) and cos(x) is 1.

Front

What is the range of sin(x) and cos(x)?

Back

The range of both sin(x) and cos(x) is [-1, 1].

Front

What is the range of tan(x)?

Back

The range of tan(x) is all real numbers (-∞, +∞).