How Do I Put Secant in My Calculator

Secant is a trigonometric function that represents the ratio of the hypotenuse to the adjacent side in a right triangle. Calculating secant values is essential in physics, engineering, and navigation. This guide explains how to put secant in your calculator and interpret the results.

How to Calculate Secant

The secant of an angle θ (sec θ) is calculated as the reciprocal of the cosine of that angle:

Secant Formula

sec θ = 1 / cos θ

To calculate secant on your calculator:

Enter the angle in degrees or radians (depending on your calculator's mode)
Press the cosine button (cos)
Press the reciprocal button (1/x or x⁻¹)

Important Note

Ensure your calculator is in the correct angle mode (DEG or RAD) before performing secant calculations. Most scientific calculators default to degrees.

Calculator Methods

Basic Scientific Calculator

For most scientific calculators:

Press the mode button to select degrees or radians
Enter the angle value
Press the cosine button (cos)
Press the reciprocal button (1/x)

Graphing Calculator

On graphing calculators like TI-84:

Press the mode button to set angle units
Enter the angle in the calculator's memory
Use the cosine function (cos)
Use the reciprocal function (1/x)

Online Calculator

Many online calculators have a dedicated secant function. Simply:

Select the angle unit (degrees or radians)
Enter the angle value
Click the secant button

Common Errors

Avoid these mistakes when calculating secant:

Using the wrong angle mode (degrees vs. radians)
Forgetting to take the reciprocal of cosine
Entering the angle in the wrong unit
Using the tangent function instead of cosine

Tip

Always double-check your calculator's mode settings before performing trigonometric calculations.

Practical Examples

Let's calculate secant for some common angles:

Angle (degrees)	Cosine Value	Secant Value
0°	1	1
30°	√3/2 ≈ 0.866	1/0.866 ≈ 1.155
45°	√2/2 ≈ 0.707	1/0.707 ≈ 1.414
60°	0.5	2
90°	0	Undefined (infinite)

Notice that secant becomes undefined at 90° because cosine is zero, making the reciprocal undefined.

FAQ

Can I calculate secant directly on my calculator?

Most scientific and graphing calculators don't have a direct secant button, but you can calculate it by finding the cosine first and then taking the reciprocal.

What's the difference between secant and cosine?

Secant is the reciprocal of cosine. While cosine gives you the ratio of adjacent to hypotenuse, secant gives you the ratio of hypotenuse to adjacent.

Why is secant undefined at 90 degrees?

At 90 degrees, cosine equals zero, and division by zero is undefined in mathematics. This means secant has no value at this angle.

How do I calculate secant in radians?

First, ensure your calculator is in radian mode, then follow the same steps as for degrees: calculate cosine and then take the reciprocal.

Can I use an online calculator for secant values?

Yes, many online calculators have a dedicated secant function. These tools are especially useful when you don't have a scientific calculator handy.