They're additionally termed as arcus functions , antitrigonometric functions or cyclometric functions. These inverse features in trigonometry are used to get the angle with any of the trigonometry ratios. The inverse trigonometry functions have predominant packages in the field of engineering, physics, geometry and navigation.
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 perform the opposite operation of the trigonometric functions such as sine, cosine, tangent, cosecant, secant, and cotangent. We know that trigonometric functions are especially applicable to the right angle triangle. These six important functions are used to find the angle measure in the 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. It is represented in the graph as shown below:
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