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

1- Trigonometric Functions

Angles complete revolution contains Example Solution

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

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

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

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

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

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

Some Trigonometric Identities:

Example Solution

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:

Theorem

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

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

Basic Properties of Natural Exponential Function

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

Basic identities

Example Prove that Solution