What are Inverse Trigonometric Functions?

Inverse trigonometric functions (also known as arcfunctions) are the inverse functions of the basic trigonometric functions like sine, cosine, and tangent. While standard trigonometric functions tell you the ratio of sides for a given angle, inverse functions allow you to work backward: given a ratio, they return the original angle.

Common notation includes using the prefix "arc" (e.g., arcsin) or a superscript "-1" (e.g., sin⁻¹). It is important to note that sin⁻¹(x) is NOT the same as 1/sin(x). The latter is the cosecant function.

How to Use This Calculator

Our inverse trigonometric calculator with steps is designed for students and professionals. Simply select the function you wish to calculate, input the numerical value (x), and choose whether you want the result in Degrees or Radians. The tool will not only provide the final answer but also explain the domain constraints and the conversion process.

Domain and Range Constraints

Because trigonometric functions are periodic, they are not naturally one-to-one. To define their inverses, their domains must be restricted:

• Arcsin: Domain is [-1, 1], Range is [-90°, 90°].
• Arccos: Domain is [-1, 1], Range is [0°, 180°].
• Arctan: Domain is all real numbers, Range is (-90°, 90°).
• Arcsec/Arccsc: Domain is |x| ≥ 1.

Frequently Asked Questions

Q: Why do I get an "Undefined" error for arcsin(2)?
A: The sine function only produces values between -1 and 1. Therefore, the inverse function arcsin(x) only exists for inputs within that range.

Q: How do I convert radians to degrees?
A: To convert from radians to degrees, multiply the value by (180 / π). Our calculator does this automatically for you in the steps section.