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4. Cotangent Calculator

θ =

DegreesRadians

Calculate

Answer: cot(θ)

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Cot Calculator is used to calculate the trigonometric cotangent of a given angle. You can specify the angle in degrees or radians. The Cot Calculator computes the cotangent of given angle and provides a step by step solution.

How to calculate cot(θ) using graph?

Step 1 - Draw unit circle

Draw a unit circle with \(O(0, 0)\) as the center of the circle on the graph paper.

Step 2 - Draw line with angle θ

Draw a line from center of the circle making an angle θ with X-axis.

Mark the point as \(P\), where the line touches the circle.

Step 3 - Form Right Angle Triangle PQO

Draw a perpendicular line from \(P\) to the X-axis.

Mark the point as \(Q\), where the perpendicular line touches the X-axis.

Now, we have a triangle, PQO with right angle at \(Q\), \(∠POQ = θ\), and \(OP = 1\) unit.

Step 4 - Calculate cot(θ)

In a right angled triangle, Cotangent of an angle (θ) is the ratio of the length of the adjacent side to the length of the opposite side.

The formula for cot(θ) is:

cot(θ) == (Length of Adjacent side)/(Length of Opposite side)

From triangle PQO,

cot(θ) == OQ/PQ

Measure the lengths \(PQ\) and \(OQ\) on the graph and find the ratio \(OQ/PQ\), that ratio is the value of cot(θ).

Print

{
  "topic": "cot",
  "function": "cot",
  "initial_value": "30",
  "function_desc": "Cotangent",
  "title": "Cotangent Calculator",
  "x_symbol": "θ",
  "x_desc": "angle",
  "tag": "Trigonometry",
  "formula": "cot(θ) = (Length of Adjacent side) / (Length of Opposite side)",
  "formula_sides": "cot(θ) = AB / BC",
  "formula_in_js": "1/Math.tan(θ)",
  "description": "Cot Calculator is used to calculate the trigonometric cotangent of a given angle. You can specify the angle in degrees or radians. The Cot Calculator computes the cotangent of given angle and provides a step by step solution.",
  "template": "calculators/trigonometry_calculator",
  "content": "<h2>How to calculate cot(θ) using graph?</h2><h3>Step <span class=\"step_number\">1</span> - Draw unit circle</h3><p>Draw a unit circle with \\(O(0, 0)\\) as the center of the circle on the graph paper.</p><img src=\"/images/trigonometry-calc-1.png\" alt=\"Cot Calculator using Graph\"/><h3>Step <span class=\"step_number\">2</span> - Draw line with angle θ</h3><p>Draw a line from center of the circle making an angle θ with X-axis.</p><img src=\"/images/trigonometry-calc-2.png\" alt=\"Cot Calculator using Graph\"/><p>Mark the point as \\(P\\), where the line touches the circle.</p><h3>Step <span class=\"step_number\">3</span> - Form Right Angle Triangle PQO</h3><p>Draw a perpendicular line from \\(P\\) to the X-axis.</p><img src=\"/images/trigonometry-calc-3.png\" alt=\"Cot Calculator using Graph\"/><p>Mark the point as \\(Q\\), where the perpendicular line touches the X-axis.</p><img src=\"/images/trigonometry-calc-4.png\" alt=\"Cot Calculator using Graph\"/><p>Now, we have a triangle, PQO with right angle at \\(Q\\), \\(∠POQ = θ\\), and \\(OP = 1\\) unit.</p><h3>Step <span class=\"step_number\">4</span> - Calculate cot(θ)</h3><p>In a right angled triangle, Cotangent of an angle (θ) is the ratio of the length of the adjacent side to the length of the opposite side.</p><p>The formula for cot(θ) is:</p><p class=\"board color3\"><span class=\"mathjs\">cot(θ) == (Length of Adjacent side)/(Length of Opposite side)</span></p><p>From triangle PQO,</p><p><span class=\"mathjs\">cot(θ) == OQ/PQ</span></p><p>Measure the lengths \\(PQ\\) and \\(OQ\\) on the graph and find the ratio \\(OQ/PQ\\), that ratio is the value of cot(θ).</p>"
}