1. What is Arcsin Function?

The arcsin function (also called inverse sine) returns the angle whose sine is the given number. It is the inverse operation of the sine function, with output in radians between -π/2 and π/2.

2. Arcsin(-1/2) Calculation

The specific calculation for arcsin(-1/2):

Explanation: The sine of -π/6 radians (-30°) is exactly -1/2, making this the principal value of the inverse sine function for this input.

3. Properties of Arcsin Function

Domain: [-1, 1]
Range: [-π/2, π/2] radians
Special Values:

• arcsin(0) = 0
• arcsin(1/2) = π/6
• arcsin(-1/2) = -π/6
• arcsin(1) = π/2
• arcsin(-1) = -π/2

4. Using the Calculator

Tips: Enter any value between -1 and 1 to calculate its arcsin. The calculator will return the result in radians and degrees.

5. Frequently Asked Questions (FAQ)

Q1: Why is arcsin(-1/2) equal to -π/6?
A: Because sin(-π/6) = -1/2, and -π/6 is within the principal range of the arcsin function.

Q2: Are there other angles with sine -1/2?
A: Yes, but arcsin returns only the principal value. Other angles include 7π/6, 11π/6, etc., but these are outside the principal range.

Q3: What is the difference between arcsin and sin⁻¹?
A: They are the same function - both represent the inverse sine function.

Q4: Can I calculate arcsin for values outside [-1, 1]?
A: No, the arcsin function is only defined for inputs between -1 and 1 inclusive.

Q5: How is arcsin related to other inverse trig functions?
A: arcsin is one of the six inverse trigonometric functions, along with arccos, arctan, arccsc, arcsec, and arccot.