Find a calculator approximation to four decimal places for each circular function value. See Example 3. cos (-1.1519)

Verified step by step guidance

1. Step 1: Understand the problem. We need to find the cosine of the angle -1.1519 radians.
2. Step 2: Recall that the cosine function is even, meaning \( \cos(-x) = \cos(x) \). Therefore, \( \cos(-1.1519) = \cos(1.1519) \).
3. Step 3: Use a calculator to find the cosine of 1.1519 radians. Ensure your calculator is set to radian mode.
4. Step 4: Enter 1.1519 into the calculator and press the cosine function button to get the approximate value.
5. Step 5: Round the result to four decimal places as required by the problem.

Key Concepts

Circular Functions

Circular functions, also known as trigonometric functions, relate the angles of a circle to the ratios of its sides. The primary circular functions include sine, cosine, and tangent, which are defined based on a unit circle. Understanding these functions is essential for evaluating angles and their corresponding values in various contexts, including negative angles.

Negative Angles

In trigonometry, negative angles are measured in the clockwise direction from the positive x-axis. The values of circular functions for negative angles can be derived using the properties of symmetry in the unit circle. For example, cos(-θ) = cos(θ), which means the cosine function is even, while sin(-θ) = -sin(θ), indicating that the sine function is odd.

Calculator Approximations

Calculator approximations involve using a scientific calculator to find numerical values of trigonometric functions to a specified degree of accuracy, such as four decimal places. This process typically requires inputting the angle in radians or degrees, depending on the calculator settings. Understanding how to use a calculator effectively is crucial for obtaining precise values for trigonometric functions.