Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles39m
- 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
Problem 29b
Textbook Question
Use a calculator to approximate the value of each expression. Give answers to six decimal places. tan 11.7689°
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1
Step 1: Understand that the problem requires finding the tangent of an angle, specifically 11.7689 degrees.
Step 2: Recall that the tangent function, \( \tan(\theta) \), is a trigonometric function that relates the angle \( \theta \) to the ratio of the opposite side to the adjacent side in a right triangle.
Step 3: Use a scientific calculator to find the tangent of 11.7689 degrees. Ensure your calculator is set to degree mode, not radians.
Step 4: Enter the angle 11.7689 into the calculator and press the tangent function button to compute the value.
Step 5: Record the result displayed on the calculator, rounding it to six decimal places as instructed.
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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 in terms of sine and cosine as tan(θ) = sin(θ) / cos(θ). Understanding this function is crucial for solving problems involving angles and their corresponding ratios.
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Calculator Functions
Using a scientific calculator effectively is essential for computing trigonometric values. Most calculators have dedicated buttons for sine, cosine, and tangent functions, and it's important to ensure that the calculator is set to the correct mode (degrees or radians) based on the angle provided. This ensures accurate results when approximating values.
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How to Use a Calculator for Trig Functions
Rounding and Precision
Rounding is the process of adjusting a number to a specified degree of accuracy. In this context, providing answers to six decimal places means that the result should be rounded to the nearest millionth. Understanding how to round numbers correctly is important for presenting precise answers in mathematical calculations.
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