Learn Trigonometry – Free Course with Videos and Guided Notes
Build a strong foundation in trigonometry with structured video lessons, guided notes, and chaptger tests. Covering angles, right triangle trigonometry, trigonometric functions, the unit circle, identities, graphing, inverse functions, and applications, this free course develops understanding and confidence through clear, step-by-step instruction.
Trigonometry Video Lessons with Guided Notes
Watch the video lessons for each section.
Download the guided notes PDF to follow along as you watch.
Engage actively by completing the notes during the lesson.
Review your completed notes as a study resource for exams.
Chapter 1 - Basic Trigonometric Concepts
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In this video, you'll learn how angles are measured using degrees and radians, the two most important units in trigonometry. We'll explore the meaning of each unit, examine how they relate to circles, and develop an understanding of why radians play such an important role in mathematics.
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In this video, you'll learn the properties of similar triangles and how they can be used to solve geometric and real-world application problems. We'll determine unknown side lengths and angle measures using proportions and explore practical examples involving similar triangles.
Chapter 2 - Right Triangle Trigonometry
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In this video, you'll learn how the six trigonometric functions relate the angles of a right triangle to ratios of its sides. We'll define sine, cosine, tangent, cosecant, secant, and cotangent, develop their reciprocal relationships, and use right triangles to evaluate each trigonometric function.
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In this video, you'll learn the special side relationships found in 45-45-90 and 30-60-90 triangles. We'll develop formulas for finding unknown side lengths, explore the exact values of related trigonometric functions, and see how these special triangles simplify many trigonometry problems.
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Chapter 3 - Trigonometric Functions
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In this video, you'll learn the fundamental ideas behind the unit circle and how it connects geometry and trigonometry. We'll review the equation of a circle, develop the equation of the unit circle, identify quadrant points, and use the unit circle equation to find coordinates of points on the circle.
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In this video, you'll learn the special angles and coordinate points that appear most frequently in trigonometry. We'll review the quadrants of the unit circle, develop the coordinates associated with 30°, 45°, and 60°, and identify the key angles and points that are essential to memorize.
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In this video, you'll learn a systematic approach for memorizing the unit circle. We'll organize the degree and radian measures of common angles, use patterns to remember their locations, and develop strategies for recalling coordinate points and quadrant signs.
▶️ Video 📝 Notes 📝 Fillable Unit Circle
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In this video, you'll learn what a reference angle is and why it plays an important role in trigonometry. We'll examine how reference angles are defined in each quadrant, develop formulas for finding them, and work through several examples involving angles measured in both degrees and radians.
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In this video, you'll learn how trigonometric functions can be extended from right triangles to real numbers using the unit circle. We'll develop the definitions of the six trigonometric functions in terms of unit circle coordinates and evaluate trigonometric functions for points on the unit circle.
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In this video, you'll learn how the signs of trigonometric functions depend on the quadrant in which an angle is located. We'll examine the signs of sine, cosine, tangent, and their reciprocal functions, introduce helpful memory aids, and use sign information to determine the location of points on the unit circle.
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In this video, you'll learn a step-by-step process for finding the exact value of trigonometric functions for angles outside the first quadrant. We'll determine quadrants, find reference angles, identify the correct signs, and evaluate trigonometric functions using special-angle values from the unit circle.
Chapter 4 - Graphs of Trigonometric Functions
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In this video, you'll learn how the sine and cosine graphs are connected to the unit circle and how they form the foundation of sinusoidal functions. We'll develop the graphs of sine and cosine, introduce amplitude, period, phase shift, and midline, and use these ideas to graph sinusoidal functions.
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In this video, you'll learn how sinusoidal functions can be used to model real-world periodic behavior. We'll analyze the motion of a Ferris wheel rider, determine the amplitude, period, phase shift, and midline of the model, and develop both sine and cosine equations that describe the rider's height over time.
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In this video, you'll learn how to graph the tangent function and identify its key features. We'll develop the graph using the unit circle, determine where tangent is undefined, locate vertical asymptotes, examine its period, and graph general tangent functions involving horizontal and vertical transformations.
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In this video, you'll learn how to graph the reciprocal trigonometric functions. We'll express cosecant, secant, and cotangent in terms of sine, cosine, and tangent, determine where each function is undefined, identify vertical asymptotes and periods, and use these properties to sketch their graphs.
Chapter 5 - Inverse Trigonometric Functions
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In this video, you'll learn what it means for a function to have an inverse and how to determine whether an inverse exists. We'll introduce one-to-one functions, use the horizontal line test to identify functions with inverses, and see how restricting the domain can create an inverse for functions that are not originally one-to-one.
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In this video, you'll learn the fundamental ideas behind inverse trigonometric functions. We'll introduce arcsine, arccosine, and arctangent, discuss why trigonometric functions require restricted domains to have inverses, examine their graphs, domains, and ranges, and develop the key properties that connect inverse trigonometric functions to their corresponding trigonometric functions.
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In this video, you'll learn how to evaluate inverse trigonometric functions using special angles and the unit circle. We'll determine exact values of inverse sine, inverse cosine, and inverse tangent functions, identify when inverse trig expressions are undefined, and use the domains and ranges of inverse trig functions to select the correct angle.
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In this video, you'll learn how trigonometric functions and inverse trigonometric functions interact through composition. We'll use inverse function properties to simplify expressions, evaluate compositions such as sin(sin⁻¹(x)) and sin⁻¹(sin(x)), determine when inverse properties apply, and use reference angles and right triangles to simplify more complicated inverse trigonometric expressions.
Chapter 6 - Trigonometric Identities
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In this video, you'll learn the most important trigonometric identities used throughout trigonometry, calculus, physics, and engineering. We'll introduce reciprocal identities, ratio identities, Pythagorean identities, periodicity identities, even-odd identities, cofunction identities, sum and difference formulas, product-to-sum formulas, sum-to-product formulas, and double-angle formulas.
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In this video, you'll learn the Pythagorean identities and how they are used to relate trigonometric functions. We'll derive the identity sin²θ + cos²θ = 1, develop equivalent forms involving tangent, secant, cotangent, and cosecant, and use these identities to determine unknown trigonometric function values.
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In this video, you'll learn how periodicity allows trigonometric functions to repeat their values. We'll determine the periods of the six trigonometric functions, develop periodicity identities, and use them to evaluate trigonometric functions involving large positive and negative angles.
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In this video, you'll learn how symmetry properties lead to important trigonometric identities. We'll define even and odd functions, identify which trigonometric functions are even or odd, develop the corresponding identities, and use them to rewrite trigonometric expressions involving negative angles.
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In this video, you'll learn how complementary and supplementary angles affect trigonometric function values. We'll define complementary and supplementary angles, develop the cofunction identities, derive supplementary angle identities, and use them to evaluate and simplify trigonometric expressions.
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In this video, you'll learn how to evaluate trigonometric functions involving sums and differences of angles. We'll develop the sum and difference formulas for sine, cosine, and tangent and use them to find exact values of trigonometric expressions that cannot be evaluated directly from the unit circle.
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In this video, you'll learn three important families of identities that are widely used in calculus, physics, and engineering. We'll develop the double-angle formulas, derive the power reduction formulas, introduce the half-angle formulas, and use each set of identities to evaluate trigonometric expressions.
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In this video, you'll learn strategies for rewriting complicated trigonometric expressions in simpler forms. We'll combine trigonometric identities with algebraic techniques such as factoring, common denominators, conjugates, and substitutions to simplify a variety of trigonometric expressions.
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In this video, you'll learn a systematic process for verifying trigonometric identities. We'll discuss how to choose the best side to work on, identify useful algebraic and trigonometric techniques, and apply a step-by-step strategy to verify a variety of increasingly challenging identities.
Chapter 7 - Trigonometric Equations
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In this video, you'll learn what trigonometric equations are and how they differ from trigonometric identities. We'll classify the major types of trigonometric equations, introduce the basic forms involving sine, cosine, and tangent, and develop a framework for solving all trigonometric equations covered in this chapter.
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In this video, you'll learn how to solve trigonometric equations that contain only one trigonometric function. We'll review the solutions of the basic equations sin θ = c, cos θ = c, and tan θ = c, use the unit circle to determine solution angles, and find both all solutions and solutions on a specified interval.
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In this video, you'll learn how to solve trigonometric equations written in quadratic form. We'll use substitution techniques to rewrite equations as quadratics, factor or solve the resulting polynomial, identify valid trigonometric solutions, and reject any extraneous values outside the range of the trigonometric function.
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In this video, you'll learn how trigonometric identities can transform difficult equations into forms that can be solved using factoring and other algebraic techniques. We'll apply Pythagorean identities, double-angle identities, and other common identities to simplify equations and find all solutions.
Chapter 8 - Additional Topics
Oblique Triangles
Polar Coordinates
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In this video, you'll learn how to convert equations between polar and rectangular form. We'll develop the relationships between polar and rectangular coordinates, identify the common forms of polar and rectangular equations, convert rectangular equations to polar equations, and convert polar equations to rectangular equations using coordinate relationships and trigonometric identities.
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Complex Numbers
Looking for completed guided notes? The notes for this course are available through the Algebra and Trigonometry note packs in the store.
Copyright & Usage
© Understand The Math LLC. All Rights Reserved. These materials are freely provided for non-commercial educational use. Redistribution is permitted with proper attribution to UnderstandTheMath.com.
Trigonometry Example Problems
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About Dr. Cheryl Hile
Understand The Math was created by Dr. Cheryl Hile, who earned a Ph.D. in Engineering Science and Applied Mathematics from Northwestern University. She has more than 25 years of experience teaching mathematics at the university level, including 20 years at Penn State. The lessons and guided notes on this site are based on materials she developed for her university courses.