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所在平台: Udemy |
课程主页: https://www.udemy.com/course/proving-verifying-and-using-trig-identities/
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Coursera 课程《三角恒等式的证明与应用》课程总结 本课程专注于三角恒等式的证明和应用。学完本课程后，您将深入理解并掌握以下三角恒等式： * 倒数恒等式与商恒等式 * 奇偶恒等式 * 余函数恒等式 * 勾股恒等式 * 和角与差角公式 * 倍角公式 * 降幂公式 * 半角公式 * 积化和差公式 * 和化积公式 您将能够运用这些恒等式来： * 证明其他三角恒等式 * 改写三角表达式 * 求出三角表达式的值 * 解三角方程 此外，课程还将教授如何证明一个三角方程**不是**恒等式。 课程内容结构清晰，每个部分都包含： 1. **阅读材料**：详细解释概念、细节及视频中使用的例题。 2. **视频演示**：提供直观的例题讲解。 通过观看视频并对照阅读材料，您将能扎实掌握三角恒等式的证明和应用。 **课程章节概览：** * **第一部分：倒数恒等式与商恒等式** * 证明与简化三角表达式 * **第二部分：奇偶恒等式** * 证明与通过奇偶性验证三角恒等式 * **第三部分：余函数恒等式** * 证明与通过余函数关系验证三角恒等式 * **第四部分：勾股恒等式** * 证明与简化、验证三角恒等式 * **第五部分：和角与差角公式** * 推导公式，证明与验证三角恒等式，求三角函数精确值 * **第六部分：倍角公式** * 证明与验证三角恒等式 * **第七部分：降幂与半角恒等式** * 证明、改写三角表达式、求三角函数精确值 * **第八部分：积化和差公式** * 证明与改写三角表达式 * **第九部分：和化积公式** * 证明与解三角方程 * **第十部分：反证法证明（Disproving Identities）** * 证明三角方程**不是**恒等式 每部分（第五部分除外，但其后也附有额外资源）的“额外内容”部分均提供手写笔记形式的概念概述和大量详细步骤的解题过程。 本课程旨在帮助您在数学学习旅程中取得进步。
This course is all about Proving/Verifying and Using Trig Identities.Upon completing this course, you will understand how to prove the Reciprocal and Quotient Identities, Odd and Even Identities, Cofunction Identities, Pythagorean Identities, Sum and Difference Formulas, Double-Angle Identities, Power Reducing Identities, Half-Angle Identities, Product-to-Sum Formulas, and Sum-to-Product Formulas. You will be able to use the above identities to verify other trig Identities, rewrite trig expressions, find the value of trig expressions, and solve trig equations.Finally, you will understand how to prove that a trig equation is NOT an identity.Section 1: The Reciprocal and Quotient IdentitiesProof of the Reciprocal and Quotient IdentitiesSimplifying Trig Expressions Using the Reciprocal and Quotient Identities The Reciprocal and Quotient Identities (Quiz)Section 2: The Odd and Even Trig IdentitiesProof of the Odd and Even Trig IdentitiesVerifying Trig Identities Using the Odd and Even Trig Identities The Odd and Even Identities (Quiz)Section 3: The Cofunction Trig Identities Proof of the Cofunction Trig IdentitiesVerifying Trig Identities Using the Cofunction Trig Identities Section 4: The Pythagorean Trig IdentitiesProving the Pythagorean Trig IdentitiesSimplifying Trig Identities Using the Pythagorean IdentitiesVerifying Trig Identities Using the Pythagorean IdentitiesThe Pythagorean Identities (Quiz)Extra: Overview of Concepts (Hand-Written)Extra: Tons of Problems Solved, Showing All Steps (Hand-Written)Section 5: The Sum and Difference FormulasDeriving the Sum and Difference Formulas for Sine and CosineProving the Sum and Difference Formulas for Tangent and CotangentVerifying Trig Identities Using the Sum and Difference Formulas Finding the Exact Value of Trig Functions Using the Sum IdentitiesThe Sum and Difference Formula (Quiz)Extra: Overview of Concepts (Hand-Written)Extra: Tons of Problems Solved, Showing All Steps (Hand-Written)Section 6: The Double Angle FormulasProving the Double Angle Identities Verifying Trig Identities Using the Double Angle FormulasThe Double-Angle Identities (Quiz)Extra: Overview of Concepts (Hand-Written)Extra: Tons of Problems Solved, Showing All Steps (Hand-Written)Section 7: The Power Reducing and Half-Angle IdentitiesProving the Power Reducing and Half-Angle IdentitiesUsing the Power-Reducing Identities to Rewrite Trig ExpressionsUsing the Half Angle Identities to Find the Exact Value of Trig ExpressionsUsing the Half-Angle Trig Identities to Find the Exact ValueThe Power Reducing and Half-Angle Identities (Quiz)Extra: Overview of Concepts (Hand-Written)Extra: Tons of Problems Solved, Showing All Steps (Hand-Written)Section 8: The Product-to-Sum FormulasProving the Product-to-Sum Trig FormulasUsing the Product-to-Sum Identities to Rewrite Trig ExpressionsThe Product-to-Sum Formulas (Quiz)Section 9: The Sum-to-Product FormulasProving the Sum to Product Trig FormulasUsing the Sum-to-Product Identities to Solve Trig EquationsThe Sum-to-Product Formulas (Quiz)Section 10: Disproving IdentitiesProving that a Trig Equation is NOT an IdentityDisproving Identities (Quiz) For each topic, you are given:1. An reading (attached as a resource) explaining concepts, details, and the example that is used in the video.2. A video showing a visual of the example in the reading.If you watch each video and follow the associated reading, you will have a good understanding for proving/verifying and using trig Identities.I hope that I can assist you on your math journey!Sincerely,MathAngel369
