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trig.docx

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Department
Mathematics
Course
MATA30H3
Professor
Ken Butler
Semester
Winter

Description
Trigonometric Functions 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 = cos kx.  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 x. -1  sec x means 1 / cos x, while cos x asks you to find an angle that has a cosine ratio equal
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