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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 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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  1. Section 5.3 Trigonometric Functions of Any Angle Objective: In this lesson you learned how to evaluate trigonometricfunctions of any angle.

  2. Important Vocabulary Define each term or concept. • Reference angles • Period

  3. I. Introduction • Let θ be an angle in standard position with (x, y) a point on the terminal side of θ and

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

  5. 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.

  6. Example 1 Θ lies in either I or IV

  7. 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

  8. II. Reference AnglesExample 2

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

  10. Example 3

  11. 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 ___________.

  12. Even and Odd • Which trigonometric functions are even functions? • Which trigonometric functions are odd functions?

  13. 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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