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 trigonometric functions of any angle. Important Vocabulary Define each term or concept. Reference angles Period. I. Introduction.

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Section 5.3 Trigonometric Functions of Any Angle

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Section 5 3 trigonometric functions of any angle

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

Important Vocabulary Define each term or concept.

  • Reference angles

  • Period


I introduction

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

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


What s your sign

What's your sign?

  • 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

Example 1

Θ lies in either I or IV


Important vocabulary define each term or concept1

Important Vocabulary 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 example 2

II. Reference AnglesExample 2


To find the value of a trigonometric function of any angle

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


Example 3

Example 3


Iii trigonometric functions of real numbers

III. Trigonometric Functions of Real Numbers

  • 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

Even and Odd

  • Which trigonometric functions are even functions?

  • Which trigonometric functions are odd functions?


Homework

Homework

  • 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


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