Calculate the secant of the angle of a right triangle. Enter the angle to calculate the ratio of the hypotenuse divided by the adjacent side of the triangle.

Secant Formula

Sec X = H/A
  • Where X is an angle in degrees or radians
  • H is the length of the hypotenuse
  • A is the length of the side adjacent to that hypotenuse

The secant can also be calculated using the inverse of the cosine.

sec x = 1 / cos x

Secant Definition

The secant is defined as the inverse of the cosine of a value.

How to calculate the secant?

The following example is a step-by-step guide on calculating the secant of an angle.

  1. First, you need to determine what information is available to you. The secant can be calculated using known trigonometric properties if the angle is known. Still, it also can be calculated through simply the equation of H/A,a where H is the length of the hypotenuse of a triangle, and A is the length of the adjacent side. For this example, we will assume the length of both of these sides is known. They will be 5m and 4m respectively.
  2. The next step is to plug these values into the above equation so sec x = 5/4 = 1.25.
  3. The last step would be to use the actual angle to check this. To do this you would need to enter the angle into the formula 1/cosx.
  4. Analyze the results.

FAQ

What is the relationship between secant and other trigonometric functions?

Secant is related to cosine as its reciprocal. It also has relationships with other trigonometric functions such as sine and tangent, through various trigonometric identities.

How do you find the secant of an angle without a calculator?

If you know the lengths of the sides of a right triangle, you can calculate the secant of one of its angles by dividing the length of the hypotenuse by the length of the adjacent side. Alternatively, if you know the cosine of the angle, take its reciprocal.

Can secant be used to solve real-world problems?

Yes, secant and other trigonometric functions are widely used in fields such as engineering, physics, architecture, and navigation to solve problems involving angles and distances.

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