Page 7 - mathematics

Transcendental Functions

1- Trigonometric Functions
2- Exponential Functions
3- Hyperbolic Functions

1- Trigonometric Functions Graph of y  sin x

y

Hypotenuse Side 1
opposite
2 3 / 2   / 2 x
  / 2  3 / 2 2

Side adjacent

sin  Side opposite csc  1 Domain: R 1
Hypotenuse sin
Range: [-1,1]
1
cos  Side adjacent sec  cos Symmetry : odd function sin x    sin x 
Hypotenuse
Zeros: ...,  3 ,  2 ,   ,0,  , 2 , 3 ,...
Side opposite sin cos 1
tan  Side adjacent  cos cot  sin  tan Periodic with period= 2π

Graph of y  cos x y Graph of y  tan x

y

1

 / 2  3 / 2 2 x x

2 3 / 2   / 2 3 / 2   / 2  / 2  3 / 2

Domain: R 1

Range: [-1,1]

Symmetry: Even function cos x   cos x  Domain:  R  zeros of cos x  Range: R

Zeros: ...,  3 / 2,   / 2,  / 2, 3 / 2,... Symmetry : Odd function tan x    tanx 

Periodic with period = 2π Zeros:  zeros of sin x Periodic with period = π

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