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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2:04 minutes

Problem 62

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. cos(30° + 20°) = cos 30° + cos 20°

Verified step by step guidance

Identify the trigonometric identity that can be used to simplify the left side of the equation: \( \cos(a + b) = \cos a \cos b - \sin a \sin b \).

Substitute \( a = 30^\circ \) and \( b = 20^\circ \) into the identity: \( \cos(30^\circ + 20^\circ) = \cos 30^\circ \cos 20^\circ - \sin 30^\circ \sin 20^\circ \).

Calculate \( \cos 30^\circ \), \( \cos 20^\circ \), \( \sin 30^\circ \), and \( \sin 20^\circ \) using a calculator.

Substitute the calculated values into the identity to find \( \cos(50^\circ) \).

Compare the result of \( \cos(50^\circ) \) with \( \cos 30^\circ + \cos 20^\circ \) to determine 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.

Cosine Addition Formula

The cosine addition formula states that cos(A + B) = cos(A)cos(B) - sin(A)sin(B). This formula is essential for accurately calculating the cosine of the sum of two angles, as it shows that the cosine of a sum is not simply the sum of the cosines of the individual angles.

Rounding Errors in Calculations

Rounding errors occur when numerical values are approximated to a certain number of decimal places, which can lead to discrepancies in calculations. In trigonometric functions, these errors can affect the precision of results, especially when dealing with angles and their trigonometric values.

Trigonometric Identities

Trigonometric identities are equations that involve trigonometric functions and are true for all values of the variables involved. Understanding these identities, such as the cosine addition formula, is crucial for simplifying expressions and solving trigonometric equations accurately.