Table of contents

0. Review of College Algebra4h 43m
1. Measuring Angles40m
2. Trigonometric Functions on Right Triangles2h 5m
3. Unit Circle1h 19m
4. Graphing Trigonometric Functions1h 19m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
6. Trigonometric Identities and More Equations2h 34m
7. Non-Right Triangles1h 38m
8. Vectors2h 25m
9. Polar Equations2h 5m
10. Parametric Equations1h 6m
11. Graphing Complex Numbers1h 7m

1. Measuring Angles

Angles in Standard Position

Trigonometry

1. Measuring Angles

Angles in Standard Position

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2:07 minutes

Problem 22

Textbook Question

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

Recognize that \( \sec \theta = \frac{1}{\cos \theta} \). Therefore, \( \sec 14.8^\circ = \frac{1}{\cos 14.8^\circ} \).

Substitute \( \sec 14.8^\circ \) into the expression: \( \frac{1}{\sec 14.8^\circ} = \cos 14.8^\circ \).

Use a calculator to find \( \cos 14.8^\circ \).

Ensure the calculator is in degree mode before calculating \( \cos 14.8^\circ \).

Round the result to six decimal places as required.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Secant Function

The secant function, denoted as sec(θ), is the reciprocal of the cosine function. It is defined as sec(θ) = 1/cos(θ). Understanding this function is crucial for simplifying expressions involving secant, as it allows you to convert secant into a more manageable form before performing calculations.

Simplification of Trigonometric Expressions

Simplifying trigonometric expressions involves using identities and relationships between trigonometric functions to rewrite them in a simpler form. This process often makes calculations easier and more straightforward, especially when using a calculator, as it reduces the complexity of the expression being evaluated.

Calculator Precision

When using a calculator to approximate values, it is important to understand the significance of precision. In this context, providing answers to six decimal places means ensuring that the final result is accurate to that level of detail, which is essential for precision in mathematical calculations and applications.

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