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

0. Review of College Algebra

Solving Linear Equations

Trigonometry

0. Review of College Algebra

Solving Linear Equations

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1:39 minutes

Problem 61

Textbook Question

Find each product or quotient where possible. See Example 2.2𝝅 2⁄3(Leave 𝝅 in the answer.)

Verified step by step guidance

Identify the expression to be simplified: \( \frac{2\pi}{\frac{2}{3}} \).

Recall that dividing by a fraction is equivalent to multiplying by its reciprocal.

Rewrite the expression as a multiplication: \( 2\pi \times \frac{3}{2} \).

Multiply the numerators together: \( 2 \times 3 = 6 \).

Multiply the result by \( \pi \) to get \( 6\pi \).

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Key Concepts

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

Radians and Degrees

Trigonometric functions can be expressed in both radians and degrees. Radians are a unit of angular measure where one full rotation is 2π radians, while degrees divide a circle into 360 parts. Understanding how to convert between these two units is essential for solving trigonometric problems, especially when dealing with angles in formulas.

Product and Quotient of Angles

In trigonometry, the product and quotient of angles refer to the multiplication or division of angle measures, which can affect the values of trigonometric functions. For example, when multiplying angles, one may use identities such as sin(a) * sin(b) or cos(a) * cos(b). Recognizing how to manipulate these products and quotients is crucial for simplifying expressions and solving equations.

Simplifying Expressions with π

When working with trigonometric expressions, it is often necessary to leave π in the answer, especially when dealing with angles expressed in radians. This means understanding how to simplify expressions while retaining π as a constant. Mastery of this concept allows for clearer communication of results and ensures accuracy in calculations involving circular functions.