Ti-86 Calculator Finding Sec of 58 Degrees and 18 Minutes

Finding the secant of an angle on a TI-86 calculator involves converting the angle to decimal degrees, calculating the cosine, and then finding the reciprocal. This guide provides step-by-step instructions, formula explanations, and practical examples to help you accurately determine the secant of 58 degrees and 18 minutes.

How to Use the TI-86 Calculator

The TI-86 calculator is a powerful scientific calculator that can perform trigonometric functions. To find the secant of an angle, you'll need to follow these general steps:

Convert the angle from degrees and minutes to decimal degrees
Calculate the cosine of the angle
Find the reciprocal of the cosine to get the secant

The calculator interface provides dedicated keys for these operations, making the process straightforward. The following sections provide detailed instructions for calculating the secant of 58°18'.

Step-by-Step Calculation

To find the secant of 58 degrees and 18 minutes using your TI-86 calculator:

Press the MODE key and select Deg to ensure the calculator is in degree mode
Enter the angle: 58.3° (since 18 minutes is 0.3 degrees)
Press the 2ND key and then the COS key to calculate the cosine
Press the 1/x key to find the reciprocal of the cosine (which gives the secant)
Press = to display the result

Tip

Remember that the secant function is the reciprocal of the cosine function. If you're working with angles in degrees and minutes, always convert them to decimal degrees first for accurate calculations.

The Secant Formula

The secant of an angle θ is defined as the reciprocal of the cosine of that angle:

Secant Formula

sec(θ) = 1 / cos(θ)

For the angle 58°18', we first convert the minutes to decimal degrees:

Angle Conversion

58°18' = 58 + (18/60) = 58.3°

Then we calculate the cosine of 58.3° and take its reciprocal to find the secant.

Worked Example

Let's calculate the secant of 58°18' step by step:

Convert 58°18' to decimal degrees: 58.3°
Calculate cos(58.3°) ≈ 0.5299
Find the reciprocal: 1 / 0.5299 ≈ 1.8879

The secant of 58°18' is approximately 1.8879. This means that if you have a right triangle with an angle of 58°18', the length of the hypotenuse is about 1.8879 times the length of the adjacent side.

Frequently Asked Questions

What is the difference between secant and cosine?: The secant function is the reciprocal of the cosine function. While cosine gives you the ratio of the adjacent side to the hypotenuse, secant gives you the ratio of the hypotenuse to the adjacent side.
How do I convert degrees and minutes to decimal degrees?: To convert degrees and minutes to decimal degrees, divide the number of minutes by 60 and add the result to the degrees. For example, 58°18' becomes 58 + (18/60) = 58.3°.
Why do I need to convert the angle before calculating the secant?: The TI-86 calculator works with decimal degrees for trigonometric functions. Converting the angle ensures accurate calculations, especially when dealing with angles that aren't whole numbers.
What if the cosine of my angle is zero?: If the cosine of an angle is zero, the secant will be undefined because division by zero is not possible. This occurs when the angle is 90° or 270°.
How can I verify my secant calculation?: You can verify your calculation by using an online trigonometric calculator or by checking the result against a scientific calculator that displays the secant function directly.