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Section 5.3 Trigonometric Functions of Any AnglePowerPoint Presentation

Section 5.3 Trigonometric Functions of Any Angle

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Section 5.3 Trigonometric Functions of Any Angle

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Section 5.3 Trigonometric Functions of Any Angle

Objective: In this lesson you learned how to evaluate trigonometricfunctions of any angle.

Important Vocabulary Define each term or concept.

- Reference angles
- Period

I. Introduction

- Let θ be an angle in standard position with (x, y) a point on the terminal side of θ and

Complete the following definitions of the trigonometric functions of any angle:

What's your sign? functions of any angle:

- Name the quadrants in which the sine function is positive.
- Name the quadrants in which the sine function is negative.
- Name the quadrants in which the cosine function is positive.
- Name the quadrants in which the cosine function is negative.
- Name the quadrants in which the tangent function is positive.
- Name the quadrants in which the tangent function is negative.

Example 1 functions of any angle:

Θ lies in either I or IV

Important Vocabulary functions of any angle:Define each term or concept.

- Reference angles
Let θ be an angle in standard position. Its reference angle is the acute angle θ’ formed by the terminal side and the horizontal axis (page 390)

- Period

II. Reference Angles functions of any angle:Example 2

To find the value of a trigonometric function of any angle functions of any angle:θ, . . .

Example 3 functions of any angle:

III. Trigonometric Functions of Real Numbers functions of any angle:

- The sine function’s domain is ______________ and its range is ___________.
- The cosine function’s domain is ____________ , and its range is _________ .
- The period of the sine function is _______. The period of the cosine function is ___________.

Even and Odd functions of any angle:

- Which trigonometric functions are even functions?
- Which trigonometric functions are odd functions?

Homework functions of any angle:

- Pg 397: #1, 3, 7, 13-19 all, 21, 23, 24, 25, 27, 29, 33, 39-53 odd
- Pg 398: #57, 59, 61, 65, 67, 69, 71, 75 77, 79, 81, 83, 85, 87, 91, 97, 99, 101, 103