Calculate tan⁻¹

x= opposite_side/adjacent_side

tan⁻¹(x)DegreesRadians

Inverse Tangent tan⁻¹() is used to find the angle for a given ratio of the length of the opposite side to the length of the adjacent side, in a right angled triangle.

Formula

To find the Inverse Tangent of a given ratio: opposite_side/adjacent_side , use the following formula.

θ = tan⁻¹(Length_of_Opposite_side / Length_of_Adjacent_side)

Calculating Tan Inverse

The inverse tangent (tan^-1 or arctan) of a value is the angle whose tangent is the given value. It is used to find angles when the tangent value is known.

The inverse tangent of a value \( y \) is defined as:

\( \tan^{-1}(y) = \theta \)

where:

\( y \) is the tangent value.
\( \theta \) is the angle in radians or degrees.

Example 1

Let's calculate the inverse tangent of 1:

The angle whose tangent is 1 is 45 degrees or \( \frac{\pi}{4} \) radians. So:

\( \tan^{-1}(1) = 45^{\circ} = \frac{\pi}{4} \)

Example 2

Consider another example with the value \( \sqrt{3} \):

The angle whose tangent is \( \sqrt{3} \) is 60 degrees or \( \frac{\pi}{3} \) radians. So:

\( \tan^{-1}(\sqrt{3}) = 60^{\circ} = \frac{\pi}{3} \)

These examples demonstrate how to calculate the inverse tangent of a value.

{ "topic": "inverse-tan", "function": "tan−1", "function_desc": "Inverse Tangent", "x_symbol": "x", "x_desc": "opposite_side/adjacent_side", "category": "Trigonometry", "formula": "θ = tan−1(Length_of_Opposite_side / Length_of_Adjacent_side)", "formula_in_js": "Math.atan(x)", "description": "Inverse Tangent tan−1() is used to find the angle for a given ratio of the length of the opposite side to the length of the adjacent side, in a right angled triangle.", "template": "trigonometry_inverse_function", "content": "<h2>Calculating Tan Inverse</h2>\nThe inverse tangent (tan-1 or arctan) of a value is the angle whose tangent is the given value. It is used to find angles when the tangent value is known.\nThe inverse tangent of a value \\( y \\) is defined as:\n\\( \\tan^{-1}(y) = \\theta \\)\nwhere:\n<ul>\n<li>\\( y \\) is the tangent value.</li>\n<li>\\( \\theta \\) is the angle in radians or degrees.</li>\n</ul>\n<h3>Example 1</h3>\nLet's calculate the inverse tangent of 1:\nThe angle whose tangent is 1 is 45 degrees or \\( \\frac{\\pi}{4} \\) radians. So:\n\\( \\tan^{-1}(1) = 45^{\\circ} = \\frac{\\pi}{4} \\)\n<h3>Example 2</h3>\nConsider another example with the value \\( \\sqrt{3} \\):\nThe angle whose tangent is \\( \\sqrt{3} \\) is 60 degrees or \\( \\frac{\\pi}{3} \\) radians. So:\n\\( \\tan^{-1}(\\sqrt{3}) = 60^{\\circ} = \\frac{\\pi}{3} \\)\nThese examples demonstrate how to calculate the inverse tangent of a value." }

Calculate tan−1

Formula

Calculating Tan Inverse

Example 1

Example 2

Trigonometry Calculators

Calculate tan⁻¹