1. Home➙
2. Calculators➙
3. Trigonometry➙
4. Secant Calculator

θ =

DegreesRadians

Calculate

Answer: sec(θ)

_

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

How to calculate sec(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 sec(θ)

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

The formula for \(sec(θ)\) is:

sec(θ) == (Length of Hypotenuse)/(Length of Adjacent side)

From triangle PQO,

sec(θ) == OP/OQ

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

sec(θ) == 1/OQ

Measure the length OQ on the graph and find \(1/OQ\), which gives the value of sec(θ).

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

Print

{
  "topic": "sec",
  "function": "sec",
  "initial_value": "30",
  "function_desc": "Secant",
  "title": "Secant Calculator",
  "x_symbol": "θ",
  "x_desc": "angle",
  "tag": "Trigonometry",
  "formula": "sec(θ) = (Length of Hypotenuse) / (Length of Adjacent side)",
  "formula_sides": "sec(θ) = AC / AB",
  "formula_in_js": "1/Math.cos(θ)",
  "description": "Sec Calculator is used to calculate the trigonometric secant of a given angle. You can specify the angle in degrees or radians. The Sec Calculator computes the secant of given angle and provides a step by step solution.",
  "template": "calculators/trigonometry_calculator",
  "content": "<h2>How to calculate sec(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=\"Sec 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=\"Cos 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=\"Cos 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=\"Cos 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 sec(θ)</h3><p>In a right angled triangle, Secant of an angle (θ) is the ratio of the length of the hypotenuse to the length of the adjacent side.</p><p>The formula for \\(sec(θ)\\) is:</p><p class=\"board color3\"><span class=\"mathjs\">sec(θ) == (Length of Hypotenuse)/(Length of Adjacent side)</span></p><p>From triangle PQO,</p><p><span class=\"mathjs\">sec(θ) == OP/OQ</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\">sec(θ) == 1/OQ</span></p><p>Measure the length OQ on the graph and find \\(1/OQ\\), which gives the value of sec(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 \\(OQ\\) with the radius of the circle before computing the inverse to get the \\(sec(θ)\\) value. For example, if you have considered 10cm as radius of the circle on the graph, then \\(OQ\\) should be divided with 10cm and then inverted to get \\(sec(θ)\\) value.</p>"
}