How this course works
The chapters and lessons below are the fixed course structure. When you start, LearnLive teaches each lesson interactively and adapts examples, pacing, and questions to you.
Complete syllabus
Every chapter and lesson
- 01
Chapter 1 · 7 lessons
Foundations of Trigonometry
- 1.1
10.1 Angles and their Measure
6 min · Quick check
Lesson goal: By the end you can understand and measure angles in degrees and radians.
- Define angles and their measures.
- Differentiate between degrees and radians.
- Convert between degrees and radians.
- Identify standard position of angles.
- Understand the concept of coterminal angles.
- 1.2
10.2 The Unit Circle: Cosine and Sine
6 min · Quick check
Lesson goal: By the end you can describe the unit circle and calculate cosine and sine values.
- Define the unit circle and its significance in trigonometry.
- Identify coordinates of key angles on the unit circle.
- Calculate cosine and sine values for angles using the unit circle.
- Understand the relationship between the unit circle and trigonometric functions.
- Visualize angles in standard position on the unit circle.
- 1.3
10.3 The Six Circular Functions and Fundamental Identities
6 min · Quick check
Lesson goal: By the end you can explain the six circular functions and fundamental identities.
- Define the six circular functions: sine, cosine, tangent, cosecant, secant, and cotangent.
- Understand the relationship between the circular functions and the unit circle.
- Identify fundamental identities involving the six circular functions.
- Apply the definitions of circular functions to find values for given angles.
- Recognize the importance of these functions in trigonometry.
- 1.4
10.4 Trigonometric Identities
6 min · Quick check
Lesson goal: By the end you can apply trigonometric identities in various contexts.
- Define trigonometric identities and their purpose.
- Identify and prove basic trigonometric identities.
- Apply identities to simplify trigonometric expressions.
- Use identities to solve trigonometric equations.
- Understand the significance of identities in trigonometric applications.
- 1.5
10.5 Graphs of the Trigonometric Functions
6 min · Quick check
Lesson goal: By the end you can graph the basic trigonometric functions accurately.
- Identify the key features of sine, cosine, and tangent graphs.
- Understand the periodic nature of trigonometric functions.
- Graph sine and cosine functions using amplitude and period.
- Graph tangent functions and understand their asymptotes.
- Analyze transformations of trigonometric graphs.
- 1.6
10.6 The Inverse Trigonometric Functions
6 min · Quick check
Lesson goal: By the end you can understand and calculate inverse trigonometric functions.
- Define inverse trigonometric functions and their domains.
- Calculate values of inverse sine, cosine, and tangent functions.
- Understand the geometric interpretation of inverse trigonometric functions.
- Identify the range of inverse trigonometric functions.
- Apply inverse functions to solve trigonometric equations.
- 1.7
10.7 Trigonometric Equations and Inequalities
6 min · Quick check
Lesson goal: By the end you can solve trigonometric equations and inequalities effectively.
- Define trigonometric equations and inequalities.
- Identify methods for solving basic trigonometric equations.
- Apply identities to solve more complex trigonometric equations.
- Understand the concept of solutions in different intervals.
- Graph solutions of trigonometric inequalities.
- 1.1
- 02
Chapter 2 · 10 lessons
Applications of Trigonometry
- 2.1
11.1 Applications of Sinusoids
6 min · Quick check
Lesson goal: By the end you can understand and apply the properties of sinusoids in real-world contexts.
- Define sinusoids and their characteristics.
- Identify applications of sinusoids in modeling periodic phenomena.
- Analyze the amplitude, period, and phase shift of sinusoidal functions.
- 2.2
11.2 The Law of Sines
6 min · Quick check
Lesson goal: By the end you can apply the Law of Sines to solve for unknown sides and angles in triangles.
- State the Law of Sines and its formula.
- Identify when to use the Law of Sines in triangle problems.
- Solve for unknown sides and angles using the Law of Sines.
- 2.3
11.3 The Law of Cosines
6 min · Quick check
Lesson goal: By the end you can apply the Law of Cosines to solve for unknown sides and angles in triangles.
- State the Law of Cosines and its formula.
- Identify when to use the Law of Cosines in triangle problems.
- Solve for unknown sides and angles using the Law of Cosines.
- 2.4
11.4 Polar Coordinates
6 min · Quick check
Lesson goal: By the end you can understand and utilize polar coordinates in representing points in a plane.
- Define polar coordinates and their relationship to Cartesian coordinates.
- Convert between polar and Cartesian coordinates.
- Graph points using polar coordinates.
- 2.5
11.5 Graphs of Polar Equations
6 min · Quick check
Lesson goal: By the end you can graph polar equations and understand their properties.
- Define polar equations and their forms.
- Identify key features of graphs of polar equations.
- Graph various types of polar equations.
- 2.6
11.6 Hooked on Conics Again
6 min · Quick check
Lesson goal: By the end you can analyze conic sections and their properties in polar coordinates.
- Define conic sections and their types.
- Identify the polar equations of conic sections.
- Analyze the properties of conic sections in polar form.
- 2.7
11.7 Polar Form of Complex Numbers
6 min · Quick check
Lesson goal: By the end you can express complex numbers in polar form and understand their applications.
- Define complex numbers and their polar representation.
- Convert complex numbers from rectangular to polar form.
- Apply polar form of complex numbers in multiplication and division.
- 2.8
11.8 Vectors
6 min · Quick check
Lesson goal: By the end you can understand and apply vector concepts in two-dimensional space.
- Define vectors and their components.
- Perform operations with vectors, including addition and scalar multiplication.
- Represent vectors graphically and algebraically.
- 2.9
11.9 The Dot Product and Projection
6 min · Quick check
Lesson goal: By the end you can calculate the dot product of vectors and understand its geometric interpretation.
- Define the dot product and its formula.
- Calculate the dot product of two vectors.
- Interpret the dot product in terms of angle and projection.
- 2.10
11.10 Parametric Equations
6 min · Quick check
Lesson goal: By the end you can analyze and graph parametric equations in two dimensions.
- Define parametric equations and their components.
- Convert parametric equations to Cartesian form.
- Graph parametric equations and analyze their behavior.
- 2.1