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4. Cosecant Calculator

θ =

DegreesRadians

Calculate

Answer: csc(θ)

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

How to calculate csc(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, using a protractor.

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 csc(θ)

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

The formula for csc(θ) is:

csc(θ) == (Length of Hypotenuse)/(Length of Opposite side)

From triangle PQO,

csc(θ) == OP/PQ

Since we have taken a unit circle, and the hypotenuse (OP) is equal the radius of the circle which is 1 unit

csc(θ) == 1/PQ

Measure the length \(PQ\) on the graph and compute the inverse of that length, which gives the value of csc(θ).

Note: If you have drawn a bigger circle on the graph, with a radius other than 1 unit, then divide the length of \(PQ\) with the radius of the circle before computing the inverse to get the \(csc(θ)\) value. For example, if you have considered 10cm as radius of the circle on the graph, then \(PQ\) should be divided with 10cm and then inverted to get \(csc(θ)\) value.

Print

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  "topic": "cosec",
  "function": "csc",
  "initial_value": "30",
  "function_desc": "Cosecant",
  "title": "Cosecant Calculator",
  "x_symbol": "θ",
  "x_desc": "angle",
  "tag": "Trigonometry",
  "formula_in_js": "1/Math.sin(θ)",
  "description": "Cosec Calculator is used to calculate the trigonometric cosecant of a given angle. You can specify the angle in degrees or radians. The Cosec Calculator computes the cosecant of given angle and provides a step by step solution.",
  "template": "calculators/trigonometry_calculator",
  "content": "<h2>How to calculate csc(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=\"Csc 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, using a protractor.</p><img src=\"/images/trigonometry-calc-2.png\" alt=\"Csc 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=\"Csc 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=\"Csc 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 csc(θ)</h3><p>In a right angled triangle, Cosecant of an angle (θ) is the ratio of the length of the hypotenuse to the length of the opposite side.</p><p>The formula for csc(θ) is:</p><p class=\"board color3\"><span class=\"mathjs\">csc(θ) == (Length of Hypotenuse)/(Length of Opposite side)</span></p><p>From triangle PQO,</p><p><span class=\"mathjs\">csc(θ) == OP/PQ</span></p><p>Since we have taken a unit circle, and the hypotenuse (OP) is equal the radius of the circle which is 1 unit</p><p><span class=\"mathjs\">csc(θ) == 1/PQ</span></p><p>Measure the length \\(PQ\\) on the graph and compute the inverse of that length, which gives the value of csc(θ).</p><p class=\"note\">Note: If you have drawn a bigger circle on the graph, with a radius other than 1 unit, then divide the length of \\(PQ\\) with the radius of the circle before computing the inverse to get the \\(csc(θ)\\) value. For example, if you have considered 10cm as radius of the circle on the graph, then \\(PQ\\) should be divided with 10cm and then inverted to get \\(csc(θ)\\) value.</p>"
}