Find a calculator approximation to four decimal places for each circular function value. See Example 3.
sec 2.8440

Verified step by step guidance

1. Recall that the secant function is the reciprocal of the cosine function. So, \( \sec x = \frac{1}{\cos x} \).
2. Identify the angle given, which is \( 2.8440 \) radians, and understand that you need to find \( \sec 2.8440 \).
3. Calculate \( \cos 2.8440 \) using a calculator set to radian mode to get an approximate value.
4. Take the reciprocal of the cosine value found in the previous step to find \( \sec 2.8440 = \frac{1}{\cos 2.8440} \).
5. Round the result to four decimal places to get the final approximation for \( \sec 2.8440 \).

Key Concepts

Circular Functions and Their Definitions

Circular functions, such as sine, cosine, and secant, are based on the unit circle. The secant function is defined as the reciprocal of the cosine function, i.e., sec(θ) = 1/cos(θ). Understanding this relationship is essential for evaluating secant values.

Using a Calculator for Trigonometric Approximations

Calculators can approximate trigonometric values by inputting the angle in radians or degrees. It is important to ensure the calculator is set to the correct mode (radians here) and to use the reciprocal function or calculate 1/cos(θ) to find sec(θ).

Rounding and Decimal Precision

When approximating values, rounding to a specified number of decimal places ensures clarity and consistency. Here, the answer should be rounded to four decimal places, which means keeping four digits after the decimal point and rounding the last digit appropriately.