How to Put Arctan in Calculator Ti 84

Introduction

The arctangent function, often written as arctan or tan⁻¹, is the inverse of the tangent function. It takes a ratio of the opposite side to the adjacent side of a right-angled triangle and returns the angle in degrees or radians. The TI-84 calculator provides this function through its trigonometric operations.

Before we dive into the steps, it's important to understand the difference between the arctan function and the tangent function. The tangent function (tan) gives you the ratio of the opposite side to the adjacent side for a given angle. The arctan function does the opposite: it gives you the angle when you know the ratio.

Step-by-Step Guide

Step 1: Access the Trigonometric Functions

To access the arctan function on your TI-84 calculator, follow these steps:

1. Turn on your TI-84 calculator.
2. Press the 2ND key.
3. Press the TAN key. This will display tan⁻¹ on the screen, indicating that you're using the arctangent function.

Step 2: Enter the Value

Once you've accessed the arctan function, you need to enter the value for which you want to find the angle. This value is typically the ratio of the opposite side to the adjacent side of a right-angled triangle.

For example, if you want to find the angle θ where tan(θ) = 0.5, you would enter 0.5.

Step 3: Specify the Angle Mode

The TI-84 calculator can work in degrees or radians. To specify the angle mode, follow these steps:

1. Press the MODE key.
2. Use the arrow keys to navigate to the Angle setting.
3. Press ENTER to select the angle mode. You can choose between degrees and radians.

Step 4: Calculate the Angle

After entering the value and specifying the angle mode, press the ENTER key to calculate the angle. The calculator will display the angle in the specified mode (degrees or radians).

Step 5: Interpret the Result

The result displayed on the calculator is the angle whose tangent is the value you entered. Make sure to note the angle mode (degrees or radians) to interpret the result correctly.

Worked Examples

Let's look at a couple of examples to see how the arctan function works on the TI-84 calculator.

Example 1: Finding an Angle in Degrees

Suppose you have a right-angled triangle where the opposite side is 3 units and the adjacent side is 4 units. You want to find the angle θ opposite the opposite side.

1. First, calculate the ratio of the opposite side to the adjacent side: 3/4 = 0.75.
2. Set your calculator to degree mode by pressing MODE and selecting Deg.
3. Access the arctan function by pressing 2ND followed by TAN.
4. Enter 0.75 and press ENTER.
5. The calculator will display approximately 36.87 degrees.

This means that the angle θ opposite the side of length 3 units is approximately 36.87 degrees.

Example 2: Finding an Angle in Radians

Now, let's consider the same triangle but find the angle in radians.

1. Calculate the ratio of the opposite side to the adjacent side: 3/4 = 0.75.
2. Set your calculator to radian mode by pressing MODE and selecting Rad.
3. Access the arctan function by pressing 2ND followed by TAN.
4. Enter 0.75 and press ENTER.
5. The calculator will display approximately 0.6435 radians.

This means that the angle θ opposite the side of length 3 units is approximately 0.6435 radians.

Troubleshooting

If you're having trouble using the arctan function on your TI-84 calculator, here are some common issues and solutions:

Issue: Calculator Doesn't Respond

If your calculator doesn't respond when you press the keys, make sure it's turned on and that the batteries are not dead. If the issue persists, try turning the calculator off and on again.

Issue: Incorrect Angle Mode

If you're getting unexpected results, double-check that your calculator is set to the correct angle mode (degrees or radians). The angle mode affects the output of the arctan function.

Issue: Wrong Function Selected

Ensure that you've selected the arctan function by pressing 2ND followed by TAN. If you accidentally press the TAN key without the 2ND key, you'll be using the tangent function instead of the arctangent function.

Issue: Incorrect Value Entered

Make sure you're entering the correct value for the arctan function. The value should be the ratio of the opposite side to the adjacent side of the right-angled triangle.