In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places.cos 𝜋10

Verified step by step guidance

1. Step 1: Recognize that the problem requires finding the cosine of an angle given in radians, specifically \( \frac{\pi}{10} \).
2. Step 2: Understand that \( \pi \) radians is equivalent to 180 degrees, so \( \frac{\pi}{10} \) radians is equivalent to \( \frac{180}{10} = 18 \) degrees.
3. Step 3: Use a calculator to find the cosine of 18 degrees. Ensure your calculator is set to degree mode if you are inputting 18 directly.
4. Step 4: If your calculator is in radian mode, input \( \frac{\pi}{10} \) directly to find the cosine value.
5. Step 5: Round the result to four decimal places as required by the problem.

Key Concepts

Trigonometric Functions

Trigonometric functions, such as sine, cosine, and tangent, relate the angles of a triangle to the lengths of its sides. They are fundamental in trigonometry and are defined for all real numbers, often using the unit circle. Understanding these functions is essential for solving problems involving angles and distances.

Calculator Use for Trigonometric Functions

Using a calculator to evaluate trigonometric functions involves inputting the angle in the correct mode (degrees or radians) and selecting the appropriate function. For example, to find cos(π/10), one must ensure the calculator is set to radians, as π is a radian measure. This process allows for precise calculations of trigonometric values.

Radian Measure

Radian measure is a way of measuring angles based on the radius of a circle. One radian is the angle formed when the arc length is equal to the radius. Understanding radians is crucial in trigonometry, especially when working with functions like cosine, as many mathematical contexts use radians instead of degrees.