Graphs of Sine, Cosine, and Tangent Functions
The graphs of y = sin x, y = cos x, and y = tan x are periodic.
The graphs of y = sin x and y = cos x are similar in shape and have an amplitude of 1 and a
period of 2π
The graph of y = sin x can be transformed into graphs modeled by equations of the form y =
sin x + c, y = sin (x – d), and y = sin kx. Similarly, the graph of y = cos x can be transformed
into graphs modeled by equations of the form y = cos x + c, y = acos x, y = cos (x – d), and y =
The graph of y = tan x has no amplitude because it has no maximum or minimum values. It is
undefined at values of x that are odd multiples of π/2, such as π/2 and 3π/2.
The graph becomes asymptotic as the angle approaches these values from left and the right.
The period of the function is π.
Graphs of Reciprocal Trigonometric Functions
The graphs of y = csc x, y = sec x, and y = cot x are periodic. They are related to the primary
trigonometric functions as reciprocal graphs.
Reciprocal trigonometric functions are different from inverse trigonometric functions.
csc x means 1 / sin x, while sin x asks you to find an angle that has a sine ratio equal to
sec x means 1 / cos x, while cos x asks you to find an angle that has a cosine ratio equal