Professor Leonard Courses

Proving the Double and Half Angle Formulas for Trigonometry

Explore proofs of double and half angle formulas for sine, cosine, and tangent, enhancing understanding of trigonometric identities and their derivations.

• YouTube
• 27 minutes
• On-Demand
• Free Video

Introduction to Sum and Difference Formulas in Trigonometry

Learn sum and difference formulas for sine, cosine, and tangent, their derivations, and applications in solving complex trigonometric problems beyond the unit circle.

• YouTube
• 51 minutes
• On-Demand
• Free Video

Introduction to Using Trigonometric Identities - Precalculus - Trigonometry

Explore basic trigonometric identities including Pythagorean, reciprocal, and even/odd identities. Learn how to apply these fundamental concepts in trigonometry and precalculus.

• YouTube
• 24 minutes
• On-Demand
• Free Video

How to Solve Trigonometric Equations - Precalculus - Trigonometry

In-depth exploration of solving trigonometric equations without inverse functions, focusing on unit circle relationships and practical problem-solving techniques.

• YouTube
• 1 hour 35 minutes
• On-Demand
• Free Video

An Indepth Look at Using Inverse Trig Functions - Precalculus - Trigonometry

Comprehensive exploration of inverse trigonometric functions, their relationship with basic trig functions, and practical applications in precalculus and trigonometry.

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Video

How to Find Inverse Trigonometric Functions - Precalculus - Trigonometry

Learn to find inverse trigonometric functions, including their domains and ranges, through a clear, step-by-step approach.

• YouTube
• 32 minutes
• On-Demand
• Free Video

How to Use Inverse Trigonometric Functions - Precalculus - Trigonometry

Explore inverse trigonometric functions, their relationship to basic trig functions, and understand their domain and range in this comprehensive tutorial.

• YouTube
• 54 minutes
• On-Demand
• Free Video

How to Graph Phase Shifts of Trigonometric Functions - Precalculus - Trigonometry

Learn to perform horizontal shifts on trigonometric functions, focusing on sine and cosine. Master phase shifts and horizontal translations applicable to all trig functions.

• YouTube
• 38 minutes
• On-Demand
• Free Video

How to Graph Cosecant and Secant - Precalculus - Trigonometry

Explore graphing secant and cosecant functions, their relationships with sine and cosine, and learn about function transformations in trigonometry.

• YouTube
• 30 minutes
• On-Demand
• Free Video

Graphing Transformations with Tangent and Cotangent - Precalculus - Trigonometry

Explore graphing techniques for tangent and cotangent functions, including vertical translation, amplitude, reflection, and period manipulation in trigonometry.

• YouTube
• 41 minutes
• On-Demand
• Free Video

Graphing Transformations with Sine and Cosine - Precalculus - Trigonometry

Learn to graph sine and cosine functions with various transformations, mastering vertical shifts, stretches, and reflections for a solid foundation in trigonometry.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Pythagorean Identities for Trigonometric Functions

Explore even, odd, and Pythagorean identities in trigonometry, their origins, and applications, with a focus on the Unit Circle and related corollaries.

• YouTube
• 38 minutes
• On-Demand
• Free Video

Reciprocal Identities in Trigonometry - Precalculus - Trigonometry

Explore reciprocal identities in trigonometry, connecting unit circle concepts with right triangle trigonometry for a deeper understanding of these fundamental relationships.

• YouTube
• 47 minutes
• On-Demand
• Free Video

Trigonometric Functions and the Unit Circle - Precalculus - Trigonometry

Explore the Unit Circle's creation, its connection to right triangle trigonometry, and the development of trigonometric functions in this comprehensive precalculus lesson.

• YouTube
• 40 minutes
• On-Demand
• Free Video

Proof by Mathematical Induction - Precalculus - College Algebra

Learn to prove summation formulas using Mathematical Induction, a powerful technique for verifying mathematical statements across infinite sets of natural numbers.

• YouTube
• 23 minutes
• On-Demand
• Free Video