1. Precalculus Functions & Graphs 5.3 B Trig Functions of Real Numbers Notes 0

2. Precalculus Functions & Graphs 5.3B Trig Functions of Real Numbers Notes 010Und1 10 1 0 00UndUnd 0UndUnd0 0010 1 10 1 0 00UndUnd 0UndUnd0 010 1 10 1 0 00UndUnd 0UndUnd0 010 1

3. Precalculus Functions & Graphs 5.3 B Trig Functions of Real Numbers Notes Repeated Value Theorem Theorem on Even and Odd Trigonometric Functions 1.The cosine and secant functions are even. 2.The sine, tangent, cotangent and cosecant functions are odd.

4. Precalculus Functions & Graphs 5.3 B Trig Functions of Real Numbers Notes Formulas for Negatives Theorem on Even and Odd Trigonometric Functions 1.The cosine and secant functions are even. 2.The sine, tangent, cotangent and cosecant functions are odd.

5. Precalculus Functions & Graphs 5.3 B Trig Functions of Real Numbers Example #1 Use a formula for negatives to find the exact value. 1 1

6. Precalculus Functions & Graphs 5.3 B Trig Functions of Real Numbers You Try #1 Use a formula for negatives to find the exact value.

7. Precalculus Functions & Graphs 5.3B Trig Functions of Real Numbers Notes Sine 010010 010 0 Notice that sin is 0 on the whole pi’s and alternating 1 and -1 on the half pi’s

8. Precalculus Functions & Graphs 5.3B Trig Functions of Real Numbers Notes Cosine 10010 010 01 Notice that cos is 0 on the half pi’s and alternating 1 and -1 on the whole pi’s

9. Precalculus Functions & Graphs 5.3B Trig Functions of Real Numbers Notes When does a function have vertical asymptotes?

10. Precalculus Functions & Graphs 5.3B Trig Functions of Real Numbers NotesCosecant The easiest way to graph this is to make the asymptotes then graph the sin function as a dotted line and put parabolas at the peaks. und1 und1 und1 und 1 und1 und1 und

11. Precalculus Functions & Graphs 5.3B Trig Functions of Real Numbers NotesSecant 1undund1 und1 und1 The easiest way to graph this is to make the asymptotes then graph the cos function as a dotted line and put parabolas at the peaks. 1undund1 und1 und1

12. Precalculus Functions & Graphs 5.3B Trig Functions of Real Numbers Notes Tangent 0und0 0 0 0 0 0 Notice that tan is 0 on the whole pi’s and asymptotes on the half pi’s

13. Precalculus Functions & Graphs 5.3B Trig Functions of Real Numbers Notes Cotangent Und0 0 0 0 0 0und Notice that tan is 0 on the whole pi’s and asymptotes on the half pi’s

14. Precalculus Functions & Graphs 5.3 B Trig Functions of Real Numbers Example #2 1 2 2

15. Precalculus Functions & Graphs 5.3 B Trig Functions of Real Numbers You Try #2 1 1 1 1

16. Precalculus Functions & Graphs 5.3 B Trig Functions of Real Numbers You Try #3 1 1 1 1

17. Precalculus Functions & Graphs 5.3 B Trig Functions of Real Numbers Example #3 Use the graph of a trigonometric function to sketch the graph of the equation without plotting points. Remember the minus two means shift the graph down 2 units the dashed red line. So the zero line for sin which is usually the x axis will be shifted down two. Recall that sin is 0 at the whole pi’s and then alternating 1 and -1. So put dots on the whole pi’s on the new zero line, and then alternate up one and down 1. Then draw the curve.