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

2. Trigonometric Functions on Right Triangles

Trigonometric Functions on Right Triangles

Trigonometry

2. Trigonometric Functions on Right Triangles

Trigonometric Functions on Right Triangles

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1:01 minutes

Problem 57

Textbook Question

Determine whether each statement is possible or impossible. See Example 4. tan θ = 0.93

Verified step by step guidance

Recall that the tangent function, \( \tan \theta \), is defined as the ratio of the opposite side to the adjacent side in a right triangle, or \( \tan \theta = \frac{\sin \theta}{\cos \theta} \).

Understand that the range of the tangent function is all real numbers, meaning \( \tan \theta \) can take any real value.

Since 0.93 is a real number, it falls within the range of possible values for \( \tan \theta \).

Therefore, the statement \( \tan \theta = 0.93 \) is possible.

Conclude that there exists an angle \( \theta \) for which \( \tan \theta = 0.93 \).

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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 can also be expressed as tan(θ) = sin(θ) / cos(θ). Understanding this function is crucial for determining the possible values of θ based on the given tangent value.

Range of the Tangent Function

The range of the tangent function is all real numbers, meaning that for any real number input, there exists a corresponding output. This characteristic implies that any value, including 0.93, can be achieved by the tangent function, making it possible to find an angle θ that satisfies tan(θ) = 0.93.

Inverse Tangent Function

The inverse tangent function, or arctan(θ), is used to find an angle when the tangent value is known. For example, if tan(θ) = 0.93, then θ can be calculated using θ = arctan(0.93). This function is essential for determining specific angles corresponding to given tangent values.