In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places.sin 38°

Verified step by step guidance

1. Step 1: Identify the trigonometric function you need to evaluate, which is \( \sin 38^\circ \).
2. Step 2: Ensure your calculator is set to degree mode, as the angle is given in degrees.
3. Step 3: Enter the angle 38 into your calculator.
4. Step 4: Press the sine function button (usually labeled as 'sin') to compute the sine of 38 degrees.
5. Step 5: Record the result displayed on the 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 sine function, specifically, is defined as the ratio of the length of the opposite side to the hypotenuse in a right triangle. Understanding these functions is essential for solving problems involving angles and distances.

Calculator Usage for Trigonometry

Using a calculator to find trigonometric values involves inputting the angle in degrees or radians, depending on the calculator's settings. For example, to find sin 38°, one must ensure the calculator is set to degree mode. This allows for accurate computation of trigonometric values, which are often required to a specific decimal place.

Rounding and Precision

Rounding is the process of adjusting a number to a specified degree of accuracy, which is crucial in trigonometry when reporting values. In this case, finding sin 38° to four decimal places means the result should be rounded to the nearest ten-thousandth. Understanding how to round correctly ensures that the final answer is both precise and meets the problem's requirements.