The document outlines the domains and ranges for various trigonometric functions, including sine, cosine, tangent, secant, cosecant, and cotangent, along with their inverse functions. It highlights which functions are one-to-one and not one-to-one, specifying the restrictions for each. Additionally, it provides mathematical representations for these functions and their inverses.

4. Trig
Fns
Domain Range Inv Trig
Functions
Domain Range
Sin x R [1,1] Sin -1
x [1,1]
Cos x R [1,1] cos -1
x [1,1]
tan x R-{x: x=(2n+1),
n
R tan -1
x R
sec x R-{x: x=(2n+1),
n
R(1,1) sec -1
x R(1,1)
cosec x R-{x: x=n,n R(1,1) cosec -1
x R(1,1)
Cot x R-{x: x=n,n R cot -1
x R

13. Not One-One
(Many one)

14. Not One-One
(Many one)
One-One

15. Not One-One
(Many one)
One-One

18. Trig
Fns
Domain Range Inv Trig
Functions
Domain Range
Sin x R [1,1] Sin -1
x [1,1]
Cos x R [1,1] cos -1
x [1,1]
tan x R-{x: x=(2n+1),
n
R tan -1
x R
sec x R-{x: x=(2n+1),
n
R(1,1) sec -1
x R(1,1)
cosec x R-{x: x=n,n R(1,1) cosec -1
x R(1,1)
Cot x R-{x: x=n,n R cot -1
x R

20. Trig
Fns
Domain Range Inv Trig
Functions
Domain Range
Sin x R [1,1] Sin -1
x [1,1]
Cos x R [1,1] cos -1
x [1,1]
tan x R-{x: x=(2n+1),
n
R tan -1
x R
sec x R-{x: x=(2n+1),
n
R(1,1) sec -1
x R(1,1)
cosec x R-{x: x=n,n R(1,1) cosec -1
x R(1,1)
Cot x R-{x: x=n,n R cot -1
x R

22. Trig
Fns
Domain Range Inv Trig
Functions
Domain Range
Sin x R [1,1] Sin -1
x [1,1]
Cos x R [1,1] cos -1
x [1,1]
tan x R-{x: x=(2n+1),
n
R tan -1
x R
sec x R-{x: x=(2n+1),
n
R(1,1) sec -1
x R(1,1)
cosec x R-{x: x=n,n R(1,1) cosec -1
x R(1,1)
Cot x R-{x: x=n,n R cot -1
x R

24. Trig
Fns
Domain Range Inv Trig
Functions
Domain Range
Sin x R [1,1] Sin -1
x [1,1]
Cos x R [1,1] cos -1
x [1,1]
tan x R-{x: x=(2n+1),
n
R tan -1
x R
sec x R-{x: x=(2n+1),
n
R(1,1) sec -1
x R(1,1)
cosec x R-{x: x=n,n R(1,1) cosec -1
x R(1,1)
Cot x R-{x: x=n,n R cot -1
x R

25. Trig
Fns
Domain Range Inv Trig
Functions
Domain Range
Sin x R [1,1] Sin -1
x [1,1]
Cos x R [1,1] cos -1
x [1,1]
tan x R-{x: x=(2n+1),
n
R tan -1
x R
sec x R-{x: x=(2n+1),
n
R(1,1) sec -1
x R(1,1)
cosec x R-{x: x=n,n R(1,1) cosec -1
x R(1,1)
Cot x R-{x: x=n,n R cot -1
x R

26. Trig
Fns
Domain Range Inv Trig
Functions
Domain Range
Sin x R [1,1] Sin -1
x [1,1]
Cos x R [1,1] cos -1
x [1,1]
tan x R-{x: x=(2n+1),
n
R tan -1
x R
sec x R-{x: x=(2n+1),
n
R(1,1) sec -1
x R(1,1)
cosec x R-{x: x=n,n R(1,1) cosec -1
x R(1,1)
Cot x R-{x: x=n,n R cot -1
x R

27. Trig
Fns
Domain Range Inv Trig
Functions
Domain Range
Sin x R [1,1] Sin -1
x [1,1]
Cos x R [1,1] cos -1
x [1,1]
tan x R-{x: x=(2n+1),
n
R tan -1
x R
sec x R-{x: x=(2n+1),
n
R(1,1) sec -1
x R(1,1)
cosec x R-{x: x=n,n R(1,1) cosec -1
x R(1,1)
Cot x R-{x: x=n,n R cot -1
x R