Inverse Trigonometric Calculator: arcsin, arccos, arctan, arcsec, arccosec, arccot
Pick a function and type a value such as 0.5, √3/2 or −1. You get the principal angle in degrees and radians, as a multiple of π when it is a standard angle.
- Nothing you type is stored
- Free
- No signup
Angle
30°
- In radians
- π/6 ≈ 0.523599
- Principal value range
- [−90°, 90°]
This is the principal value; other angles with the same ratio differ by full turns or lie in another quadrant.
Show working
- x = 0.5
- arcsin(0.5) = 30° = π/6 rad
How to use
- Choose arcsin, arccos, arctan, arccosec, arcsec or arccot.
- Type the value, e.g. 1/2, √3/2 or 0.3.
- Read the angle in degrees and radians.
Good to know
Principal value ranges (as in NCERT Class 12): arcsin [−90°, 90°], arccos [0°, 180°], arctan (−90°, 90°), arccosec [−90°, 90°] except 0, arcsec [0°, 180°] except 90°, arccot (0°, 180°).
Domains: arcsin and arccos accept only −1 to 1; arcsec and arccosec need |x| ≥ 1. arctan and arccot accept any real number.
arccosec x = arcsin(1/x) and arcsec x = arccos(1/x). arccot x = arctan(1/x) for x > 0, plus 180° for x < 0, so the answer stays between 0° and 180°.
Questions
What is arcsin(1/2)?
30°, which is π/6 radians.
Why does arcsin(2) give an error?
sin θ is never more than 1, so there is no angle whose sine is 2.
Can I type √3/2?
Yes. Values with √, fractions and π are understood, e.g. √3/2, 1/√2 or −1/2.
Are there other angles with the same value?
Yes, infinitely many (add multiples of 360°, or use the other quadrant). The calculator gives the principal value.
Is my data stored or sent anywhere?
No. The calculation runs entirely in your browser; nothing you type leaves your device.