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.
1/ sec 14.8°

Verified step by step guidance

1. Recall the definition of the secant function: \(\sec \theta = \frac{1}{\cos \theta}\). This means that \(\frac{1}{\sec \theta} = \cos \theta\).
2. Rewrite the given expression \(\frac{1}{\sec 14.8^\circ}\) as \(\cos 14.8^\circ\) using the identity from step 1.
3. Use a calculator to find the value of \(\cos 14.8^\circ\). Make sure your calculator is set to degree mode since the angle is given in degrees.
4. Calculate the cosine value and round the result to six decimal places as requested.
5. Write down the final answer with six decimal places, ensuring the approximation is clear and precise.

Key Concepts

Understanding the Secant Function

The secant function, sec(θ), is the reciprocal of the cosine function, defined as sec(θ) = 1/cos(θ). Knowing this relationship allows you to rewrite expressions involving secant in terms of cosine, which is often easier to evaluate using a calculator.

Simplifying Trigonometric Expressions

Simplifying expressions before calculation helps reduce errors and makes the evaluation process straightforward. For example, rewriting 1/sec(θ) as cos(θ) simplifies the expression and avoids dealing with complex reciprocal values directly.

Using a Calculator for Trigonometric Values

Calculators typically provide trigonometric functions like sine, cosine, and tangent. To find values like cos(14.8°), ensure the calculator is set to degree mode, input the angle correctly, and round the result to the required decimal places for precision.