What is the formula of inverse trigonometric functions?
Christopher Anderson
Published Feb 19, 2026
What is the formula of inverse trigonometric functions?
Table of Inverse Trigonometric Functions
| Function Name | Notation | Definition |
|---|---|---|
| Arccosine or inverse cosine | y=cos-1(x) | x=cos y |
| Arctangent or Inverse tangent | y=tan-1(x) | x=tan y |
| Arccotangent or Inverse Cot | y=cot-1(x) | x=cot y |
| Arcsecant or Inverse Secant | y = sec-1(x) | x=sec y |
What are the six inverse trigonometric functions?
Inverse trigonometric functions are simply defined as the inverse functions of the basic trigonometric functions which are sine, cosine, tangent, cotangent, secant, and cosecant functions.
How do you solve inverse trigonometry questions?
Problems on Inverse Trigonometric Function
- Find the values of sin (cos−1 3/5)
- Let, cos−1 3/5 = θ
- Therefore, sin θ = √(1 – cos2 θ) = √(1 – 9/25) = √(16/25) = 4/5 .
- Therefore, sin (cos−1 3/5) = sin θ = 4/5.
- Find the values of tan−1 sin (- π/2)
What is the formula of a inverse?
For a matrix A, its inverse is A-1, and A.A-1 = I. Let us check for the inverse of matrix, for a matrix of order 2 × 2, the general formula for the inverse of matrix is equal to the adjoint of a matrix divided by the determinant of a matrix.
Is arc cosine the same as inverse cosine?
The arccos function is the inverse of the cosine function. It returns the angle whose cosine is a given number. Use arccos when you know the cosine of an angle and want to know the actual angle.
Is arcsin and sin 1 the same?
What if we have to find just the measure of angle θ? The inverse sine function or Sin-1 takes the ratio, Opposite Side / Hypotenuse Side and produces angle θ. It is also written as arcsin. Let us see an example of inverse of sine function.
Which inverse trigonometric function has a range of 0 pi?
inverse cosine function
The domain of the inverse cosine function is [−1,1] and the range is [0,π] .
What is the main difference between a trig function and its inverse?
The idea is the same in trigonometry. Inverse trig functions do the opposite of the “regular” trig functions. For example: Inverse sine ( sin − 1 ) (\sin^{-1}) (sin−1)left parenthesis, sine, start superscript, minus, 1, end superscript, right parenthesis does the opposite of the sine.
What is the inverse trigonometric ratio of sine?
Inverse Trigonometric Ratios Table
| Trigonometric Ratios | Inverse Trigonometric Ratios |
|---|---|
| sin 0 = 0 | sin−10 = 0 |
| sin(π/6) =1/2 | sin−1(1/2) = π/6 |
| sin(π/4) = 1/√2 | sin−1(1/√2) = π/4 |
| sin(π/3) = √3/2 | sin−1(√3/2) = π/3 |
What is the formula for inverse trigonometric functions?
The basic inverse trigonometric formulas are as follows: Inverse Trig Functions. Formulas. Arcsine. sin-1(-x) = -sin-1(x), x ∈ [-1, 1] Arccosine. cos-1(-x) = π -cos-1(x), x ∈ [-1, 1] Arctangent. tan-1(-x) = -tan-1(x), x ∈ R.
Do inverse trigonometric functions pass the horizontal line test?
Graphs of Inverse Trigonometric Functions Trigonometric functions are all periodic functions . Thus the graphs of none of them pass the Horizontal Line Test and so are not 1 − to − 1 .
What is the domain and range of inverse circular functions?
Principal values, domains of inverse circular functions and range of inverse trig functions: S. No. Function Domain Range 1. y = sin-1x -1 ≤ x ≤ 1 -π/2 ≤ y ≤ π/2 2. y = cos-1x -1 ≤ x ≤ 1 0 ≤ y ≤ π 3. y = tan-1x x ∈ R -π/2 < x < π/2 4. y = cot-1x x ∈ R 0 < y < π
What is the value of the inverse of cos 1 3?
Since cosine is the ratio of the adjacent side to the hypotenuse, the value of the inverse cosine is 30 °, or about 0.52 radians. cos − 1 (3 2) = 30 ° Graphs of Inverse Trigonometric Functions Trigonometric functions are all periodic functions.
