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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1:37 minutes

Problem 57

Textbook Question

In Exercises 55–58, use a calculator to find the value of the acute angle θ to the nearest degree.tan θ = 4.6252

Verified step by step guidance

Identify the trigonometric function given in the problem, which is \( \tan \theta = 4.6252 \).

To find the angle \( \theta \), use the inverse tangent function, also known as \( \arctan \) or \( \tan^{-1} \).

Set up the equation \( \theta = \tan^{-1}(4.6252) \).

Use a calculator to compute \( \tan^{-1}(4.6252) \). Ensure the calculator is set to degree mode.

Round the result to the nearest degree to find the value of the acute angle \( \theta \).

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Key Concepts

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

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 is crucial for solving problems involving angles and sides in right triangles, and it is periodic with a period of π radians (or 180 degrees). Understanding how to manipulate and interpret the tangent function is essential for finding angles from given ratios.

Inverse Trigonometric Functions

Inverse trigonometric functions, such as arctan or tan⁻¹, are used to determine the angle when the value of a trigonometric function is known. For example, if tan(θ) = 4.6252, we can find θ by calculating θ = arctan(4.6252). These functions are vital for solving equations where the angle is the unknown, allowing us to reverse the process of finding the tangent of an angle.

Calculator Usage for Trigonometric Functions

Using a calculator to find trigonometric values involves understanding how to input functions correctly and interpret the results. Most scientific calculators have dedicated buttons for trigonometric functions and their inverses. It is important to ensure that the calculator is set to the correct mode (degrees or radians) based on the context of the problem, as this will affect the output angle.