About This Chapter
Understanding Trigonometry - Chapter Summary
The lessons in this chapter provide an overview of trigonometry. You'll learn about the different kinds of trigonometric identities, how to use complex numbers in polar form, what a restricted domain means, and more. After completing the chapter, you should be able to:
- Solve trigonometric equations using trigonometric identities and inverses
- Use inverse operations to simplify equations
- Solve trigonometric equations with restricted domains and infinite solutions
- Analyze the vertices, base, and height of a triangle
- Explain why inverse trigonometric functions have a limited range
- Combine complex numbers using addition, subtraction, and multiplication
- Detail how roots of unity are used
For video lessons, the timelines let you easily navigate to specific topics. You can review all the lessons in order, or just look at the ones that cover the topics you need to review. A brief multiple-choice quiz is available with each lesson to test your knowledge. If you get stuck on a topic, use the Help tab to submit questions to our expert instructors.
1. Trigonometric Identities: Definition & Uses
After watching this video lesson, you will understand what a trigonometric identity is. You will also know the different kinds of identities you will come across.
2. Solve Trigonometric Equations with Identities & Inverses
After watching this video lesson, you will be able to solve trigonometric equations by making use of trigonometric identities and inverses. Learn the steps to take to get to your solution.
3. How to Solve Trigonometric Equations for X
Adding trigonometric functions into standard algebra equations adds complexity. Learn how to solve trigonometric equations for x and how to use inverse operations to simplify equations.
4. Solving Trigonometric Equations with Restricted Domains
After watching this video lesson, you will be able to find the right answer for a trigonometric equation with a restricted domain. Learn what it means to have a restricted domain and what you need to do to find your answer.
5. Solving Trigonometric Equations with Infinite Solutions
Watch this video lesson and you will learn that all trigonometric equations have an infinite set of solutions. But you will also see that we can still go ahead and solve our equations and find concrete answers.
6. Triangles: Definition and Properties
What makes a shape a triangle? In this lesson, we'll explore the definition of a triangle, then analyze the parts of triangles, including the vertices, base and height.
7. Properties of Inverse Trigonometric Functions
After watching this video lesson, you will understand why our inverse trigonometric functions have a limited range. Learn what this does. Also learn the notation for these functions.
8. What is a Complex Number? - Definition & Properties
Applications of complex numbers include signal processing filters in engineering and vector length calculations in physics. After defining complex numbers, this lesson explores how to combine them using addition, subtraction and multiplication.
9. Complex Numbers in Polar Form: Process & Examples
After watching this video lesson, you will be able to convert complex numbers from rectangular form to polar form easily by following the formulas you will see here. You will also learn how to find the power of a complex number.
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Other chapters within the UPSEE Paper 1: Study Guide & Test Prep course
- Basics of Scientific Units & Measurement
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- Energy, Work & Power in Physics
- Fundamentals of Linear Momentum
- Understanding Rotation of a Rigid Body
- Gravitation in Physics
- Understanding Oscillatory Motion
- Mechanics of Solids & Fluids
- Properties of Heat & Thermodynamics
- Overview of Waves
- Understanding Electrostatics
- Overview of Current Electricity
- Magnetic Effect of Current
- Magnetism in Matter
- Electromagnetic Induction Overview
- Ray Optics & Optical Instruments
- Understanding Wave Optics
- Overview of Modern Physics
- Overview of Nuclear Physics
- Electronics, Transistors & Signals
- Atomic Structure & Configuration
- Properties of Chemical Bonds
- Redox Reactions Overview
- Chemical Equilibrium & Kinetics
- Electrochemistry & Catalysts
- Colloids in Chemistry
- Colligative Properties of Solution
- Periodic Table & Electronic Configuration
- Overview of Thermochemistry
- Reactions & Compounds in Organic Chemistry
- Understanding Isomerism
- Overview of Organic Compounds
- Properties of Solids in Chemistry
- Overview of Algebra Basics
- Matrices in Algebra
- Probability in Math
- Overview of Coordinate Geometry
- Principles of Calculus
- Vectors in Algebra
- Mechanics Overview
- UPSEE Paper 1 Flashcards