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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1:43 minutes

Problem 51

Textbook Question

Use a calculator to determine whether each statement is true or false. A true statement may lead to results that differ in the last decimal place due to rounding error. sin 10° + sin 10° = sin 20°

Verified step by step guidance

Step 1: Understand the problem. We need to verify if the equation \( \sin 10^\circ + \sin 10^\circ = \sin 20^\circ \) is true.

Step 2: Simplify the left side of the equation. Since \( \sin 10^\circ + \sin 10^\circ \) is the same as \( 2 \sin 10^\circ \), rewrite the left side as \( 2 \sin 10^\circ \).

Step 3: Compare the simplified left side \( 2 \sin 10^\circ \) with the right side \( \sin 20^\circ \).

Step 4: Use a calculator to find the numerical values of \( 2 \sin 10^\circ \) and \( \sin 20^\circ \).

Step 5: Determine if the values from Step 4 are equal, which will tell us if the original statement is true or false.

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Key Concepts

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

Trigonometric Identities

Trigonometric identities are equations that involve trigonometric functions and are true for all values of the variables involved. One important identity is the sine addition formula, which states that sin(a + b) = sin(a)cos(b) + cos(a)sin(b). This identity is crucial for understanding how to manipulate and simplify expressions involving sine functions.

Rounding Errors

Rounding errors occur when numerical values are approximated to a certain number of decimal places, leading to slight inaccuracies in calculations. In trigonometry, using a calculator can introduce rounding errors, especially when dealing with angles and their sine values. Understanding how these errors can affect the results is essential for interpreting the accuracy of trigonometric calculations.

Sine Function Properties

The sine function is a periodic function that relates the angle of a right triangle to the ratio of the length of the opposite side to the hypotenuse. It has specific properties, such as sin(0°) = 0 and sin(90°) = 1. Additionally, the sine function is not linear, meaning that sin(a) + sin(b) does not equal sin(a + b) unless specific conditions are met, which is key to evaluating the given statement.