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
3. Unit Circle
Trigonometric Functions on the Unit Circle
2:24 minutes
Problem 77
Textbook Question
Textbook QuestionFind a formula for the area of each figure in terms of s.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Area of a Triangle
The area of a triangle can be calculated using the formula A = 1/2 * base * height. However, when the lengths of the sides are known, Heron's formula can be used, which states that the area A is given by A = β(s(s-a)(s-b)(s-c)), where s is the semi-perimeter and a, b, c are the lengths of the sides.
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Semi-Perimeter
The semi-perimeter of a triangle is defined as half of the perimeter. It is calculated as s = (a + b + c) / 2, where a, b, and c are the lengths of the triangle's sides. The semi-perimeter is a crucial component in Heron's formula for calculating the area of a triangle.
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Heron's Formula
Heron's formula provides a way to calculate the area of a triangle when the lengths of all three sides are known. It utilizes the semi-perimeter and is expressed as A = β(s(s-a)(s-b)(s-c)). This formula is particularly useful for triangles where height is not easily determined.
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Related Practice
Textbook Question
Find exact values of the six trigonometric functions for each angle A.
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Trigonometric Functions on the Unit Circle practice set
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