Inverse Sine Calculator
Trigonometric inverse sine calculator
# What is inverse sine?
Inverse sine is the inverse of basic sine function. In the sine function, value of angle θ is taken to give the ratio opposite/hypotenuse. However, inverse sine function takes the ratio opposite/hypotenuse and gives angle θ.
sin-1 (opposite/hypotenuse) = θ
Inverse sine symbol
Inverse sine is represented as sin-1 or arcsin.
# Inverse sine rule
The rule for inverse sine is derived from the rule of sine function which is:
a/sin(A) = b/sin(B) = c/sin(C)
Now, we’ll derive the rule for side a, the rule for the remaining sides will be exactly the same
a/sin(A) = k
a = sin (A) k
Taking sin-1 on both sides
sin-1 a = sin-1 [sin (A) * k]
sin-1 a = k
Here, k represents any given constant value
# Inverse sine table
| x | Deg. Degrees | Rad. Radians |
|---|---|---|
| arcsin(-1.0) | -90.00 |
-1.57
-π / 2 |
| arcsin(-0.9) | -64.15 | -1.11 |
| arcsin(-0.8) | -53.13 | -0.92 |
| arcsin(-0.7) | -44.42 | -0.77 |
| arcsin(-0.6) | -36.86 | -0.64 |
| arcsin(-0.5) | -30.00 |
-0.52
-π / 6 |
| arcsin(-0.4) | -23.57 | -0.41 |
| arcsin(-0.3) | -17.45 | -0.30 |
| arcsin(-0.2) | -11.53 | -0.20 |
| arcsin(-0.1) | -5.73 | -0.10 |
| arcsin(0.0) | 0.00 | 0.00 |
| arcsin(0.1) | 5.73 | 0.10 |
| arcsin(0.2) | 11.53 | 0.20 |
| arcsin(0.3) | 17.45 | 0.30 |
| arcsin(0.4) | 23.57 | 0.41 |
| arcsin(0.5) | 30.00 |
0.52
π / 6 |
| arcsin(0.6) | 36.86 | 0.64 |
| arcsin(0.7) | 44.42 | 0.77 |
| arcsin(0.8) | 53.13 | 0.92 |
| arcsin(0.9) | 64.15 | 1.11 |
| arcsin(1.0) | 90.00 |
1.57
π / 2 |