Use a calculator to approximate the value of each expression. Give answers to six decimal places. In Exercises 21–28, simplify the expression before using the calculator. See Example 1. tan(-80° 06')

Key Concepts

Tangent Function

The tangent function, denoted as tan(θ), is a fundamental trigonometric function defined as the ratio of the opposite side to the adjacent side in a right triangle. It can also be expressed in terms of sine and cosine as tan(θ) = sin(θ) / cos(θ). Understanding how to manipulate this function is essential for simplifying expressions involving angles.

Angle Measurement

Angles can be measured in degrees or radians, with degrees being the more common unit in everyday contexts. In this question, the angle is given in degrees and minutes, where -80° 06' represents a negative angle in the fourth quadrant. Converting between degrees and radians or understanding how to interpret angles in different formats is crucial for accurate calculations.

Calculator Functions

Modern calculators can compute trigonometric functions, but it's important to ensure that the calculator is set to the correct mode (degrees or radians) based on the angle measurement. Additionally, knowing how to input angles in degrees and minutes correctly is vital for obtaining precise results, especially when rounding to a specific number of decimal places.