Many trigonometry functions are there that have their inverse. While getting the inverse of a trigonometric function, we will have to look at the co-domain and domain. Some trigonometric functions are sin x, cos x, tan x, etc.
Trigonometric functions
Some trigonometric functions are discussed below:
- Sin x, Tan x, Cos x, Cot x, Cosec x, and sec x.
- When we do the inverse of these functions then it totally gets changed.
- sin-1(-x) = -sin-1x,x ∈ [-1,1]
- tan-1(-x) = -tan-1x, x ∈ R
- cosec-1(-x) = -cosec-1x, or x ∈ R - (-1,1)
- cos-1(-x) = π - cos-1x, or x ∈ [-1,1]
- sec-1(-x) = π - sec-1x, or x ∈ R - (-1,1)
- cot-1(-x) = π - cot-1x, or x ∈ R
Complementary functions formulas
The complementary inverse of the trigonometric functions gets with the right angle result.
- Like the inverse of a complementary inverse, trigonometric functions are always equal to the right angle.
- When we do the inverse of these functions then it totally gets changed.
- It is that the sum of the sine-cosine, cot-tan, tan-cot are always equal to π/2.
- LIKE sin-1x + cos-1x = π/2, or x ∈ [-1,1]
- tan-1x + cot-1x = π/2, or x ∈ R
- sec-1x + cosec-1x = π/2, or x ∈ R - [-1,1]