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Enter the tangent value, and the free Arctan Calculator will determine the inverse tangent (arctan) value in both degrees and radians.
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The free online arctan calculator lets you find the inverse tangent function, \( \arctan(x) \), in radians, degrees, and other units. Enter a tangent value, and the tool handles the calculations automatically. It supports decimals like 0.5, 0.86, -0.9, etc.
In trigonometry, the arctangent is the inverse of the tangent function. For a real number \( x \in \mathbb{R} \):
If \( \tan(y) = x \), then \( \arctan(x) = y = \tan^{-1}(x) \).
Using an online arctan calculator is the most convenient way to handle inverse tangent calculations.
\( y = \tan(x) \quad \Rightarrow \quad x = \arctan(y) \)
If \( \tan(45^\circ) = 1 \), then:
\( \arctan(1) = \tan^{-1}(1) = 45^\circ = 45 \times \pi / 180 \approx 0.7854 \, \text{rad} \)
To find an angle from tangent:
\( \theta = \arctan\left(\frac{\text{opposite}}{\text{adjacent}}\right) = \arctan(a/b) \)
Example: Right-angled triangle with opposite side \( a \) and adjacent side \( b \):
These values are useful for manual calculations, though a calculator can simplify the process:
| y | arctan(y) (°) | arctan(y) (rad) |
|---|---|---|
| -∞ | -90° | -π/2 |
| -√3 | -60° | -π/3 |
| -1 | -45° | -π/4 |
| -√3/3 | -30° | -π/6 |
| 0 | 0° | 0 |
| √3/3 | 30° | π/6 |
| 1 | 45° | π/4 |
| √3 | 60° | π/3 |
| ∞ | 90° | π/2 |
The arctan function starts at \( (-\infty, -\pi/2) \) and approaches \( (\infty, \pi/2) \):
An arccos calculator works similarly for inverse cosine.
Limiting arctan to \( [-\pi/2, \pi/2] \) ensures it is one-to-one. Adding 180° accounts for angles in quadrants 2 and 3.
Since the range is \( [-\pi/2, \pi/2] \), \( \arctan(\infty) = \pi/2 = 90^\circ \).
No, the series diverges as x grows large, similar to the harmonic series.
\( \arctan(-\infty) = -90° \), lying in the fourth quadrant.
The arctan calculator simplifies one of the trickiest trigonometric functions. It is ideal for students and teachers to learn and verify inverse tangent calculations easily.
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