In trigonometric features, the arctangent represents the inverse tangent feature of x. in this phenomenon, ( x ) is real ( (x ∈ ℝ)). To calculate arctan when the tangent of ( y ) is equal to ( x ), it suggests that ( tan y = x). on this circumstance the arctangent of x can be same to the inverse tangent characteristic of ( x), therefore ( y arctan x= tan-1 x = y). but, the maximum handy manner to address this inverse trigonometric characteristic is to apply a tan inverse calculator.
To discover the inverse of tangent you may use its following method:
$$ y = tan(x) | x = arctan(y) $$
Also, you can use the arctan calculator for calculating inverse tangent, as opposed to the usage of the above formula.
Example
If the tangent of \( 30^\circ \) is equal to \( \frac{1}{\sqrt{3}} \), then:
$$ \arctan \left(\frac{1}{\sqrt{3}}\right) = \tan^{-1} \left(\frac{1}{\sqrt{3}}\right) = 30^\circ $$
$$ 30^\circ = 30 \times \frac{\pi}{180} = \frac{\pi}{6} \, \text{radians} $$
The usage of an inverse tangent calculator is the excellent manner to finish the calculation that involves taking the inverse of tangent. It allows you discover the arctan in tiers, radians, and relevant gadgets. If the arctan of ( frac{1}{sqrt{3}} ) is 30 levels, then to discover the inverse tangent, talk to the following calculations:
$$ \arctan \left(\frac{1}{\sqrt{3}}\right) = \tan^{-1} \left(\frac{1}{\sqrt{3}}\right) = 30^\circ $$
$$ = 30^\circ + k \times 180^\circ \quad (k = -1,0,1,...) $$
$$ = -150^\circ, 30^\circ, 210^\circ, ... $$
$$ = \frac{\pi}{6} \, \text{radians} + k \times \pi \quad (k = -1,0,1,...) $$
$$ = -\frac{5\pi}{6}, \frac{\pi}{6}, \frac{7\pi}{6}, ... $$
For greater accuracy, you can use an unit circle point calculator to discover the corresponding trigonometric functions on the unit circle.
To discover an perspective using the inverse tangent characteristic manually, use the formulation:
$$ \arctan(\theta) \quad \text{or} \quad \tan^{-1}(\theta) $$
$$ \tan(\theta) = \frac{a}{b} $$
$$ \theta = \arctan \left( \frac{a}{b} \right) $$
Inverse tan Calculator makes the calculation faster and errors-unfastened. To recognize it, you just need to comply with the step defined beneath:
Input
Output
The inverse tan calculator calculates:
including a hundred and eighty ranges to arc tangent as it isn't always viable to have a feature of 1 to many. therefore, proscribing the theta from \( \frac{-π}{2} to \frac{π}{2}\) guarantees that the inverse tangent a one-to-one characteristic. on this manner, you could get inverse tangent on quadrant 1 and four.
because the variety of inverse tangent is from \( \frac{-π}{2} to \frac{π}{2}\) so tan inverse(infinity) could be equal to= \( \frac {π}{2} Tan90°.
No, it does not converge. within the case of arctan1x, as x receives larger, the collection will become the harmonic series, which best diverges as opposed to converging.
