Inverse Trigonometric Functions: Overview, Questions, Preparation

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Inverse Trigonometric Functions Inverse Laplace Transform Inverse Cosine Inverse Sine Derivative of Inverse Trigonome...

Rajdeep Das

Updated on Jul 29, 2021 02:15 IST

Table of Contents

Inverse trigonometric functions
Inverse Trigonometric Functions
Formulas
Tables
Inverse Trigonometric Functions Properties

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	− π/2 ≤ y ≤ π/2 -90°≤ y ≤ 90°
Arccosine or inverse cosine	y=cos-1(x)	x=cos y	−1 ≤ x ≤ 1	0 ≤ y ≤ π 0° ≤ y ≤ 180°
Arctangent or Inverse tangent	y=tan-1(x)	x=tan y	For all real numbers	− π/2 -90°
Arccotangent or Inverse Cot	y=cot-1(x)	x=cot y	For all real numbers	0 0°
Arcsecant or Inverse Secant	y = sec-1(x)	x=sec y	x ≤ −1 or 1 ≤ x	0≤y 0°≤y
Arccosecant	y=csc-1(x)	x=csc y	x ≤ −1 or 1 ≤ x	−π/2≤y −90°≤y

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?

A: To locate the reverse of an equation, for example, sin x = 1/2, settle for the accompanying assertion: “x is equivalent to the point whose sine is 1/2.” In the trig talk, you compose this assertion as x = sin–1(1/2).

Q: What are the six functions of inverse trig?

A: They are precisely the inverses of the functions of sine, cosine, tangent, cotangent, secant, and cosecant. They are used to derive an angle from each of the trigonometric ratios of the angles.

Q: Is SEC the inverse of cos?

A: The secant is the equivalent of cosine. It is the proportion of the hypotenuse to the side neighbouring a given point in a right triangle.

Q: What is the converse of Cot 1?

A: The backward of the cotangent function is called inverse cotangent or arccot. It is meant by cot-1x. The area and scope of arccot work is - ∞

Q: What is the inverse of cosine called?

A: The inverse of cosine is called arccosine.