Question

syallubus for inverse trignometry​

Answer 1

Answer:

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. They are also termed as arcus functions, antitrigonometric functions or cyclometric functions. These inverse functions in trigonometry are used to get the angle with any of the trigonometry ratios. The inverse trigonometry functions have major applications in the field of engineering, physics, geometry and navigation.

Table of Contents:

Definition

Formulas

Graphs

Table

Derivatives

Properties

Examples

What are Inverse Trigonometric Functions?

Inverse trigonometric functions are also called “Arc Functions” since, for a given value of trigonometric functions, they produce the length of arc needed to obtain that particular value. The inverse trigonometric functions actually performs the opposite operation of the trigonometric functions such as sine, cosine, tangent, cosecant, secant, and cotangent. We know that, trig functions are specially applicable to the right angle triangle. These six important functions are used to find the angle measure in a right triangle when two sides of the triangle measures are known.

Formulas

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

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

Inverse Trigonometric  Functions Graphs

There are particularly six inverse trig functions for each trigonometry ratio. The inverse of six important trigonometric functions are:

Arcsine

Arccosine

Arctangent

Arccotangent

Arcsecant

Arccosecant

Let us discuss all the six important types of inverse trigonometric functions along with its definition, formulas, graphs, properties and solved examples.

Arcsine Function

Arcsine function is an inverse of the sine function denoted by sin-1x.