91Ó°ÊÓ

When dealing with trigonometric functions like tangent, it's crucial to ensure that your calculator is set to the correct angle measurement mode. Many calculators are equipped with two modes: degree mode and radian mode.

For problems featuring angles expressed in degrees, such as in this exercise with \(304^\circ\), the calculator must be in degree mode.

• Degree mode: Used when angles are given in degrees.
• Radian mode: Used when angles are expressed in radians.

Switching between modes is typically done via a "Mode" button on your calculator. Navigating through mode settings allows you to select the appropriate angle measure. It's good practice to double-check this setting before performing calculations to avoid errors.

Angles in real-world applications are often given in degrees, making understanding of degree mode essential for accurate computations.

The tangent function, denoted as \( \tan \), is a fundamental trigonometric function. It's part of a group known as the primary trigonometric functions, alongside sine and cosine.

The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side. Mathematically, this is expressed as:

\[\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\]
In terms of the unit circle, tangent can also be defined using sine and cosine:\[\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}\]
This dual perspective—through right triangles and the unit circle—makes tangent versatile for solving a variety of problems.

Understanding tangent is important not only for solving textbook exercises but also for applying these concepts in fields like engineering and physics, where angles and their functions play crucial roles.

A calculator is an essential tool for evaluating trigonometric functions like tangent, especially when dealing with non-standard angles. Here's how you can effectively use a calculator for this task:

• Ensure the calculator is in the correct mode—degree mode in this instance.
• Identify the function button: Look for the "tan" button on your calculator. This is how you'll input the tangent function.
• Input the angle: For \( \tan 304^\circ \), type the sequence \( \tan \) followed by \( 304 \).

Press 'Enter' or 'Equals' to get the result. Once you have the result, remember the rounding rule—round your answer to four decimal places, as specified in the exercise. This means adjusting the calculated decimal value slightly to fit the format required—in this case, count to the fourth digit after the decimal point and round up or down according to standard rounding rules.

Understanding how to use your calculator efficiently enhances speed and accuracy in solving trigonometric problems.