Inverse trigonometric functions
Inverse geometrical functions are characterised as the backward elements of the fundamental mathematical functions—sine, cosine, tangent, cotangent, secant, and cosecant functions. They are also called arcus functions, anti-trigonometric functions, or cyclometric functions.
These inverse functions in geometry are used to get the point with any of the geometry proportions. The opposite geometry functions have significant applications in designing, material science, calculation, and route.
Inverse Trigonometric Functions
Inverse mathematical functions are likewise called “Arc Functions” since they produce the length of bend expected to acquire that specific worth for a given estimation of geometrical functions. The converse geometrical functions play out the contrary activity of the mathematical functions, for example, sine, cosine, digression, cosecant, secant, and cotangent. We realise that mathematical functions are particularly material to the correct point triangle. These six significant functions are used to discover the point measure in the correct triangle when different sides of the triangle measures are known.
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Formulas
| 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 |
| Arccotangent |
cot-1(-x) = π – cot-1(x), x ∈ R |
| Arcsecant |
sec-1(-x) = π -sec-1(x), |x| ≥ 1 |
| Arccosecant |
cosec-1(-x) = -cosec-1(x), |x| ≥ 1 |
Tables
Allow us to rework all the opposite trigonometric functions with their documentation, definition, space, and reach.
| Function Name |
Notation |
Definition |
Domain of x |
Range |
|---|---|---|---|---|
| Arcsine or inverse sine |
y = sin-1(x) |
x=sin y |
−1 ≤ x ≤ 1 |
|
| Arccosine or inverse cosine |
y=cos-1(x) |
x=cos y |
−1 ≤ x ≤ 1 |
|
| Arctangent or Inverse tangent |
y=tan-1(x) |
x=tan y |
For all real numbers |
|
| Arccotangent or Inverse Cot |
y=cot-1(x) |
x=cot y |
For all real numbers |
|
| Arcsecant or Inverse Secant |
y = sec-1(x) |
x=sec y |
x ≤ −1 or 1 ≤ x |
|
| Arccosecant |
y=csc-1(x) |
x=csc y |
x ≤ −1 or 1 ≤ x |
|
Inverse Trigonometric Functions Properties
The backward geometrical functions are otherwise called Arc functions. Inverse trigonometric functions are characterised in a specific stretch (under confined spaces).
Trigonometry Basics
Inverse fundamentals incorporate the essential geometry and geometrical proportions, for example, sin x, cos x, tan x, cosec x, sec x, and bed x.
Inverse Trigonometric Functions in Class 12
Inverse Trigonometric Functions comes under the unit “Relations and Functions” in Class 12, which carries 10 marks in exams.
Frequently Asked Questions (FAQs)
Q: How would you settle backward trig functions?
Q: What are the six functions of inverse trig?
Q: Is SEC the inverse of cos?
Q: What is the converse of Cot 1?
Q: What is the inverse of cosine called?
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