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

5. Inverse Trigonometric Functions and Basic Trigonometric Equations

Inverse Sine, Cosine, & Tangent

Trigonometry

5. Inverse Trigonometric Functions and Basic Trigonometric Equations

Inverse Sine, Cosine, & Tangent

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1:41 minutes

Problem 35

Textbook Question

In Exercises 27–38, use a calculator to find the value of each expression rounded to two decimal places.tan⁻¹ (−20)

Verified step by step guidance

Understand that \( \tan^{-1}(x) \) is the inverse tangent function, which gives the angle whose tangent is \( x \).

Recognize that \( \tan^{-1}(-20) \) will yield an angle in the fourth quadrant because the tangent function is negative in the fourth quadrant.

Use a calculator to find \( \tan^{-1}(-20) \). Ensure your calculator is set to the correct mode (degrees or radians) as required by your problem context.

Round the result from the calculator to two decimal places.

Verify the angle is in the correct quadrant by considering the properties of the tangent function and its inverse.

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Key Concepts

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

Inverse Trigonometric Functions

Inverse trigonometric functions, such as tan⁻¹ (arctangent), are used to find the angle whose tangent is a given number. For example, tan⁻¹(x) returns the angle θ such that tan(θ) = x. This is crucial for solving problems where the angle is unknown and is often used in various applications, including physics and engineering.

Calculator Functions

Using a calculator to evaluate trigonometric functions requires understanding how to input values correctly. Most scientific calculators have dedicated buttons for inverse functions, allowing users to compute angles directly. Familiarity with the calculator's interface and settings, such as degree or radian mode, is essential for obtaining accurate results.

Rounding Numbers

Rounding numbers is a mathematical process used to simplify a number to a specified degree of accuracy. In this context, rounding to two decimal places means adjusting the result of the calculation to the nearest hundredth. This is important for presenting results clearly and concisely, especially in practical applications where precision is necessary.