In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places.tan 32.7°

Verified step by step guidance

1. Step 1: Identify the trigonometric function you need to evaluate, which is \( \tan(32.7^\circ) \).
2. Step 2: Ensure your calculator is set to degree mode, as the angle provided is in degrees.
3. Step 3: Enter the angle 32.7 into your calculator.
4. Step 4: Use the tangent function key (often labeled as 'tan') on your calculator to find the tangent of 32.7 degrees.
5. Step 5: Record the result displayed on your calculator, rounding it to four decimal places.

Key Concepts

Trigonometric Functions

Trigonometric functions, such as sine, cosine, and tangent, relate the angles of a triangle to the lengths of its sides. The tangent function, specifically, is defined as the ratio of the opposite side to the adjacent side in a right triangle. Understanding these functions is essential for solving problems involving angles and distances in trigonometry.

Calculator Use for Trigonometric Functions

Using a calculator to find trigonometric function values involves inputting the angle in degrees or radians, depending on the calculator's settings. For the tangent function, you would enter the angle (in this case, 32.7°) and select the tangent function to obtain a numerical value. Familiarity with calculator functions is crucial for accurately computing trigonometric values.

Rounding and Precision

Rounding and precision are important in mathematics, especially when reporting results. In this context, the problem specifies finding the tangent of 32.7° to four decimal places, which means the result should be rounded to four digits after the decimal point. Understanding how to round numbers correctly ensures that the final answer is both accurate and meets the required precision.