2. Chapter (3) Transcendental Functions 1- Trigonometric Functions 2- Exponential Functions 3- Hyperbolic Functions

3. 1- Trigonometric Functions

4. Angles complete revolution contains Example Solution

5. Domain: R Range: [-1,1] Symmetry : odd function Zeros: Periodic with period= 2π

6. Domain: R Range: [-1,1] Symmetry: Even function Zeros: Periodic with period = 2π

7. Domain:Range: R Symmetry : Odd function Zeros: Periodic with period = π

8. Domain:Range: R Symmetry : Odd function Zeros: Periodic with period = π

9. Domain: R- zeros of sin x Range: R- (-1,1) Symmetry : odd function No ZerosPeriodic with period= 2π

10. Domain: R- zeros of cosx Range: R- (-1,1) Symmetry : even function No ZerosPeriodic with period= 2π

11. Some Trigonometric Identities:

12. Example Solution

13. 2- Exponential Functions The exponential function is a function of the form a >0, a ≠ 1 In the definition of an exponential function, a, the base, is required to be positive. Domain: Range:

14. Theorem

15. Example Solution (i) Evaluate the limit (ii) Sketch the graph of the function

16. The Natural Exponential Function The value of e accurate to eight places is 2.71828183.

17. Basic Properties of Natural Exponential Function

18. 3- Hyperbolic Functions The hyperbolic functions are some combinations of and arise so frequently in mathematics and its applications.

20. Basic identities

21. Example Prove that Solution