The document discusses the domains and ranges of various trigonometric and inverse trigonometric functions. It outlines the ranges for functions like sine, cosine, tangent, secant, cosecant, and cotangent, along with their inverses. Additionally, it highlights the one-to-one and many-to-one properties of these functions.

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