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Goal: To use inverse trig functions to help us solve equations. Recall: A function is a set of ordered pairs (inputs and outputs) such that no two different ordered pairs have the same first coordinate. A function passes the Vertical Line Test. We usually symbolize y as a function of x by 1. y = f(x). A function is one-to-one if no two different ordered pairs have the same second coordinate. A one-to-one function passes the Horizontal Line Test. 2. The inverse of a function f is obtained by switching the first and second coordinates in all the ordered pairs that comprise f. The inverse of f is denoted by f 3. The domain and range of f and f are flip-flopped. 4. Section 6.5: Inverse Trigonometric Functions Saturday, September 6, 2014 11:27 PM Section 6.5 Inverse Trigonometric Functions Page 1

Section 6.5: Inverse Trigonometric Functions 115 PDF...2. The inverseof a function f is obtained by switching the first and second coordinates in all the ordered pairs that comprise

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Page 1: Section 6.5: Inverse Trigonometric Functions 115 PDF...2. The inverseof a function f is obtained by switching the first and second coordinates in all the ordered pairs that comprise

Goal: To use inverse trig functions to help us solve equations.

Recall:

A function is a set of ordered pairs (inputs and outputs) such that no two different ordered pairs have the same first coordinate. A function passes the Vertical Line Test. We usually symbolize y as a function of x by

1.

y = f(x).A function is one-to-one if no two different ordered pairs have the same second coordinate. A one-to-one function passes the Horizontal Line Test.

2.

The inverse of a function f is obtained by switching the first and second coordinates in all the ordered pairs that comprise f. The inverse of f is denoted by f

3.

The domain and range of f and f are flip-flopped.4.

Section 6.5: Inverse Trigonometric FunctionsSaturday, September 6, 201411:27 PM

Section 6.5 Inverse Trigonometric Functions Page 1

Page 2: Section 6.5: Inverse Trigonometric Functions 115 PDF...2. The inverseof a function f is obtained by switching the first and second coordinates in all the ordered pairs that comprise

Section 6.5 Inverse Trigonometric Functions Page 2

Page 3: Section 6.5: Inverse Trigonometric Functions 115 PDF...2. The inverseof a function f is obtained by switching the first and second coordinates in all the ordered pairs that comprise

Section 6.5 Inverse Trigonometric Functions Page 3

Page 4: Section 6.5: Inverse Trigonometric Functions 115 PDF...2. The inverseof a function f is obtained by switching the first and second coordinates in all the ordered pairs that comprise

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Page 5: Section 6.5: Inverse Trigonometric Functions 115 PDF...2. The inverseof a function f is obtained by switching the first and second coordinates in all the ordered pairs that comprise

Section 6.5 Inverse Trigonometric Functions Page 5

Page 6: Section 6.5: Inverse Trigonometric Functions 115 PDF...2. The inverseof a function f is obtained by switching the first and second coordinates in all the ordered pairs that comprise

Section 6.5 Inverse Trigonometric Functions Page 6

Page 7: Section 6.5: Inverse Trigonometric Functions 115 PDF...2. The inverseof a function f is obtained by switching the first and second coordinates in all the ordered pairs that comprise

Section 6.5 Inverse Trigonometric Functions Page 7

Page 8: Section 6.5: Inverse Trigonometric Functions 115 PDF...2. The inverseof a function f is obtained by switching the first and second coordinates in all the ordered pairs that comprise

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Section 6.5 Inverse Trigonometric Functions Page 8