Problem 36 - 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. $$. \cos 57^{\circ}$$

Step-by-Step Solution

Answer

The value of \( \cos 57^{\circ} \) rounded to four decimal places is approximately 0.5446.

Step 1: Set the Calculator Mode

Initially, check or set the mode of the calculator to DEGREE. Every calculator may have a slightly different process to do this. Therefore, it's necessary to refer to the calculator's manual if unsure.

Step 2: Perform the Calculation

After setting the calculator's mode, key in 'cos 57' on the calculator and press the 'EQUALS' button.

Step 3: Reading and Rounding off the Result

On pressing 'EQUALS', a decimal number will be displayed. Mark it down and then round this number to four decimal places. Remember, if the fifth number is 5 or above it should be rounded up and if it's less than 5, it's rounded down.

Key Concepts

Scientific Calculator

A scientific calculator is an essential tool for solving various mathematical problems, especially those involving trigonometry. Unlike a simple calculator, it is equipped with specialized functions and keys that help with complex calculations. These calculators can handle trigonometric functions such as sine, cosine, and tangent. This is particularly relevant for the task of evaluating cosine, which requires specific steps to ensure accuracy. Using a scientific calculator simplifies the process of calculating trigonometric values, as manual computations can be lengthy and error-prone.

• They eliminate the need for trigonometry tables.
• Provide quick and precise answers.

Understanding how to operate a scientific calculator efficiently is vital, and referring to its manual can be a helpful way to master its functions.

Degree Mode

When dealing with trigonometric functions in real-world applications, it’s crucial to use the correct measurement mode on your calculator. There are two primary angle measurements: degrees and radians. For most school and day-to-day applications, **Degree Mode** is used. It's accessible through your calculator’s mode settings. This setting ensures that the calculator interprets your input as degrees.

• Switching to Degree Mode is necessary, especially when angles are given in degrees.
• A calculator in Radian Mode will provide different, usually incorrect, results when dealing with angle measurements meant for Degree Mode.

Always ensure that your calculator is set to the correct mode for the task at hand to avoid errors in your results.

Rounding Numbers

Rounding numbers is an essential skill when working with decimal results in trigonometry. Once you calculate a trigonometric function using the **Scientific Calculator**, you may end up with a long decimal number. Rounding this to a defined number of decimal places makes it easier to read and use.

• Four decimal places provide a balance between precision and practicality.
• To round off: examine the digit following your target decimal place.
• If it's 5 or higher, round the last digit up; if it's less than 5, leave it unchanged.

Rounding helps simplify numbers for reporting results, ensuring consistency and clarity in presentations or further calculations.