Let be a right angled triangle, with let
Then, .
The lengths are known as respectively.
Definiton 1
(i)
(ii)
(iii)
(iv)
(v)
(vi)
We also defined:
(i)
(ii)
(iii)
(iv)
Definition 2
For angle-measure we defined:
,
,
are not defined.
Definition 3
For angle- measure we defined
are not defined.
Note:
have not defined as rations of lengths. So we do not use the term ‘trigonometric ratio’ for them. We shall replace the term by more general term ‘trigonometric function.’
Trigonometric Function for
Let denote respectively the x-coordinates and y-coordinates of a point whose polar coordinates are
Definitions
(i) Sine :
(ii) Cosine:
(iii) Tangent:
(iv) Cotangent:
(v) Secant:
(vi) Cosecant:
Note:
By taking in the above definitions we get the trigonometric functions from a unit circle.
Domain and Range of Trigonometric Functions
Domain | Range | |
(i) | ||
(ii) | ||
(iii) | ||
(iv) | ||
(v) | ||
(vi) |