Use a calculator to approximate each value in decimal degrees.
θ = arcsec 3.4723155

Key Concepts

Arcsecant Function

The arcsecant function, denoted as arcsec or sec^-1, is the inverse of the secant function. It is defined for values of x where |x| ≥ 1, and it returns an angle θ such that sec(θ) = x. Understanding this function is crucial for solving problems involving angles derived from secant values.

Calculator Functions

Using a scientific calculator effectively is essential for approximating trigonometric values. Most calculators have specific functions for inverse trigonometric operations, including arcsec. Familiarity with how to input values and interpret results in decimal degrees is necessary for accurate calculations.

Degrees vs. Radians

Trigonometric functions can be expressed in degrees or radians, which are two different units for measuring angles. In this context, the question specifies decimal degrees, so it is important to ensure that the calculator is set to the correct mode to avoid conversion errors when interpreting the results of the arcsec function.