How to Do Tan of Degrees on Calculator

Calculating the tangent of an angle in degrees is a fundamental trigonometric operation used in many fields including engineering, physics, and navigation. This guide explains how to perform this calculation using both a calculator and manual methods, along with common angle values and practical applications.

How to Calculate Tan of Degrees

The tangent of an angle in a right-angled triangle is the ratio of the length of the opposite side to the length of the adjacent side. For any angle θ, the tangent can be calculated using the formula:

tan(θ) = opposite / adjacent

When working with degrees, you'll need to ensure your calculator is set to degree mode before performing the calculation. This guide covers both calculator methods and manual calculation techniques.

Using a Calculator

Step-by-Step Instructions

Turn on your calculator and ensure it's in degree mode (not radian mode).
Enter the angle in degrees that you want to calculate the tangent for.
Press the "tan" button on your calculator.
The calculator will display the tangent of the angle.

Tip: Most scientific calculators have a mode switch that allows you to toggle between degrees and radians. Always verify your calculator is in degree mode before performing trigonometric calculations.

Example Calculation

Let's calculate tan(30°):

Set calculator to degree mode.
Enter 30.
Press the tan button.
The result will be approximately 0.577.

Manual Calculation

For angles where you know the opposite and adjacent sides, you can calculate the tangent manually:

tan(θ) = opposite / adjacent

Example Problem

In a right-angled triangle, if the opposite side is 4 units and the adjacent side is 6 units, what is the tangent of the angle?

Identify the opposite and adjacent sides: 4 and 6.
Divide the opposite by the adjacent: 4/6 = 0.6667.
The tangent of the angle is approximately 0.6667.

Common Angle Values

Here are the tangent values for common angles in degrees:

Angle (degrees)	Tangent Value
0°	0
30°	√3/3 ≈ 0.577
45°	1
60°	√3 ≈ 1.732
90°	Undefined (approaches infinity)

Note: The tangent function is undefined at 90° because the adjacent side length becomes zero, making the division operation undefined.

FAQ

Why is my calculator giving different results for tan(30°)?: Ensure your calculator is in degree mode. If it's in radian mode, you'll get different results. Most calculators have a mode switch or a dedicated degree button.
What happens if I try to calculate tan(90°)?: The tangent function approaches infinity as the angle approaches 90°. Most calculators will display "Error" or "Undefined" for tan(90°).
Can I use the tangent function for angles greater than 90°?: Yes, but you need to consider the angle's position in the unit circle. The tangent function is periodic with a period of 180°, so tan(θ) = tan(θ + 180°n) where n is an integer.
How accurate are calculator results for tangent?: Modern scientific calculators provide results with high precision, typically to 10 decimal places or more. For most practical purposes, this level of accuracy is sufficient.
Is there a relationship between tangent and sine/cosine?: Yes, the tangent function can be expressed as the ratio of sine to cosine: tan(θ) = sin(θ)/cos(θ). This relationship is fundamental in trigonometry.