Inverse Trigonometric Functions Calculator

Inverse Trigonometric Calculator is an excellent tool for calculating the values of inverse trigonometric functions. The result of the calculation can be in degrees or radians.

Inverse Trig Functions Calculator

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What are inverse trigonometric functions?

Inverse trigonometric functions are inverse functions of trigonometric functions. It does the opposite of trigonometric functions. Input the trigonometric ratio and output the angle in radians. In addition to mathematics, inverse trigonometric functions are widely used in engineering, navigation, physics, geometry and other fields. There are usually two representations, one is the beginning of arc + function name, such as arcsine, arctan, etc. The other is -1 power, such as sin^-1(x), cos^-1(x), etc. They both represent inverse trigonometric functions.

Since trigonometric functions are periodic, their inverse function is multi-valued, which cannot satisfy the requirement that one variable corresponds to one function value. Therefore, to make the trigonometric functions have inverse functions, they can only take values in the monotone interval. For example, the inverse function of sine in [-π2, π2] is called the arcsine function, denoted as arcsin.

y = arcsin(x)

x ∈ [-1,1]

y ∈ [-π2, π2]

The inverse function of the cosine function y = cos(x) on [0, π] is called the arccosine function.

y = arccos(x)

x ∈ [-1,1]

y ∈ [0, π]

In addition to arcsine and arccosine, there are four common inverse trigonometric functions, namely: arctan, arccot, arcsec and arccsc. Their domains and ranges are different, summarized below

Function	Notation	Definition	Domain	Range
arcsin	y = arcsin(x)	x = sin(y)	-1 ≤ x ≤ 1	-π2 ≤ y ≤ π2
arccos	y = arccos(x)	x = cos(y)	-1 ≤ x ≤ 1	0 ≤ y ≤ π
arctan	y = arctan(x)	x = tan(y)	all real numbers	-π2 < y < π2
arccot	y = arccot(x)	x = cot(y)	all real numbers	0 < y < π
arcsec	y = arcsec(x)	x = sec(y)	x ≤ -1 or x ≥ 1	0 ≤ y ≤ π and y ≠ π2
arccsc	y = arccsc(x)	x = csc(y)	x ≤ -1 or x ≥ 1	-π2 ≤ y ≤ π2 and y ≠ 0

Why do you need inverse trigonometric functions?

As we all know, inverse trigonometric functions are generally used to express, and rarely calculated directly. If you want to calculate inverse trigonometric functions, you must borrow a trigonometric function table or an inverse trigonometric function calculator.

For example, sin(30°) = 0.5. what is the arcsine of 0.5?

arcsin(0.5) = 30°

Another example, tan(45°) = 1. what is the arctan of 1?

arctan(1) = tan^-1(1) = 45°

Here are simple examples. If you encounter some complex numbers, you must use an inverse trigonometric functions calculator to calculate the results. That’s why we developed the Inverse Trig Calculator. With its help, you can easily calculate the values of inverse trigonometric functions.

How to use inverse trig functions calculator

Inverse trig functions Calculator is easy to use, 3 steps:

First, select inverse trig functions type. Including arcsine, arccosine, arctangent, arccotangent, arcsecant and arccosecant.

Second, enter the value. Make sure to be in the domain of inverse trigonometric functions.

Third, click Calculate button to get the inverse trigonometric function value, or click Reset button to start a new calculation.

FAQS

Q: What are inverse trig functions used for?
A: The most common use of inverse trigonometric functions is to find angles based on trigonometric ratios. For example, in a right triangle, the ratio of the opposite side to the hypotenuse of the acute angle is 0.5, then according to the inverse trigonometric function, the degree of the acute angle can be calculated to be 30°

Q: What is the inverse trigonometric function of cosine?
A: The inverse trigonometric function of cosine is arccosine. Abbreviated as arccos(x) or cos^-1(x).

Q: Why does the computed inverse trigonometric function not exist?
A: Usually, the input value is not in the definition domain of the inverse trigonometric function, so the calculated result does not exist.

Q: Is the result of the calculation in degrees or radians?
A: By default, both degrees and radians will be displayed, please save the result according to actual needs.

Q: What are the inputs and outputs of inverse trigonometric functions?
A: Inverse trigonometric functions take real numbers as input and output as degrees or radians.

Conclusion

In general, inverse trigonometric functions are more difficult to compute than trigonometric functions. But the practical application of inverse trigonometric functions is no less than that of trigonometric functions. Therefore, it is very important to learn to calculate inverse trigonometric functions. If you can’t, use the inverse trig calculator on this page to help you.