Problem 38 - Precalculus : Building Concepts and Connections

Question

Use a scientific calculator to evaluate the trigonometric functions. Make sure the calculator is in DEGREE mode. Round to four decimal places. \(.\) tan \(17^{\circ}\)

Step-by-Step Solution

Answer

The exact answer will depend on your calculator model, but using standard scientific calculators, the result for tan \(17^{\circ}\) rounded to four decimal places is approximately 0.3057.

Step 1: Setting up calculator

First, it is necessary to ensure the calculator is in DEGREE mode, this is usually done through the calculator's settings.

Step 2: Inputting the function to be evaluated

Then, look for the tan button on the calculator, input \(17^{\circ}\) after the tan function.

Step 3: Evaluating the function

Once the expression is typed out on the calculator, press the = button to get the final answer.

Step 4: Rounding the answer

Finally, round the answer to the closest four decimal places if necessary.

Key Concepts

Evaluating Trigonometric Functions with a Scientific Calculator

Mastering the use of a scientific calculator is key when dealing with trigonometric functions like the tangent, sine, or cosine. These calculators come equipped with specific buttons for these operations, each designed to handle the functions at the press of a key. Understanding your scientific calculator's layout and functionality is paramount. Begin by locating the trigonometric function buttons, often marked as 'sin', 'cos', and 'tan'. These buttons allow for direct input of angles to calculate their corresponding trigonometric values.

It's crucial to familiarize yourself with the calculator's instruction manual to exploit its full potential. Different models may have varying input methods - some require you to enter the angle first, followed by pressing the trigonometric function button, while others work the opposite way. Being consistent with this process ensures accuracy and can significantly streamline the problem-solving experience.

Degree Mode Calculation in Trigonometry

When working with angles in trigonometry, it's essential to understand the difference between degree and radian modes on your calculator. Most trigonometric problems will specify which unit is being used. For calculations that involve degrees, your calculator must be set to 'Degree' mode. This mode interprets the angle inputs as degrees.

To set your calculator to Degree mode, look for a button or menu that allows you to switch between 'DEG', 'RAD', and sometimes 'GRAD' – representing degrees, radians, and gradians, respectively. Selecting 'DEG' ensures that when you input an angle, the calculator will use the degree measurement to evaluate the trigonometric function. Always double-check the mode before beginning, as using the wrong mode will lead to incorrect results. For example, when entering the angle for \( tan 17^{\text{\textdegree}} \) make sure the display or setting reads 'DEG' to get the correct tangent value for 17 degrees.

Rounding Decimal Places for Precision

The practice of rounding decimal places is crucial for achieving the desired precision in mathematical calculations. When rounding to a specific number of decimal places, you look at the digit immediately after your rounding threshold. If this digit is five or greater, you round the last retained digit up. Otherwise, you leave it as is.

For instance, if you are rounding to four decimal places and your calculator displays \( 0.123456 \), the fifth decimal place is a '5', which means you would round up the fourth place giving you \( 0.1235 \). Why four decimal places? In many scientific contexts, four decimal places strike a balance between precision and practicality, minimizing rounding errors without overcomplicating calculations. Remember, when solving homework or applying this to real-world problems, adhere to the specified decimal place requirement for consistency and accuracy.