Become a Trigonometry & Precalculus Master from Udemy

) and an additional 10 workbooks with extra practice problems, to help you test your understanding along the way. Become an Trigonometry & Precalculus Master is organized into the following sections:

Angles and their measure, including degrees, DMS, and radians
Angles in circles, including oriented arcs, circular sectors, and linear and angular velocity
The six circular functions, which are sine, cosine, tangent, cosecant, secant, and tangent
The laws of sine and cosine, including Heron's formula
The unit circle, and how to use it to complete a triangle
Graphing the trig functions using period and amplitude, horizontal and vertical shifts, and other transformations
Trig identities like even-odd, sum-difference, double-angle, half-angle, product-to-sum, and sum-to-product
Inverse trig functions and their graphs
Polar coordinates and graphing polar curves
Complex numbers, including polar forms and De Moivre's Theorem
Matrices for solving systems, Gauss-Jordan elimination, transformations and inverse matrices
Partial fractions, distinct and repeated, linear and quadratic factors
Conic sections and analytic geometry of circles, ellipses, parabolas, and hyperbolas
Parametric curves and how to sketch their graphs

AND HERE' We start from the beginning... I explain the problem setup and why I set it up that way, the steps I take and why I take them, how to work through the yucky, fuzzy middle parts, and how to simplify the answer when you get it.

Notes: The notes section of each lesson is where you find the most important things to remember. It’s like Cliff Notes for books, but for math. Everything you need to know to pass your class and nothing you don’t.

Quizzes: When you think you’ve got a good grasp on a topic within a course, you can test your knowledge by taking one of the quizzes. If you pass, great. If not, you can review the videos and notes again or ask for help in the Q&A section.

Workbooks: Want even more practice? When you've finished the section, you can review everything you've learned by working through the bonus workbook. The workbooks include tons of extra practice problems, so they're a great way to solidify what you just learned in that section.

HERE' I feel like I am actually learning something from them. " - Jon K.

“The Instructor has an excellent command of the subject material and a great way of presenting it. In addition to that, she has a very pleasant voice that keeps you attentive.” - Robert S.

“This is an excellent course to become more familiar with trigonometric equations. The step by step instruction is very is to follow. I found it very helpful to follow along with solving the problems on paper to solidify the learning experience.” - David M.

“Krista explains everything in "simplest terms" so even if you haven't worked with this stuff for a while, she makes it totally easy to get back into the swing of it all. Thanks for (another) excellent course. ” - Paul L.

“Huge help to be able to review these in a platform much more suited to learning than YouTube.” - Wesley F.

YOU'

I can't wait for you to get started on mastering trigonometry and precalculus.

- Krista :)

What's inside

Learning objectives

Angles and their measure, including degrees, dms and radians
Six circular functions, including sine, cosine, tangent, cosecant, secant, and cotangent
The unit circle, including finding sine and cosine, and how to complete a triangle
Angles in circles, including oriented arcs, circular sectors, and linear and angular velocity
Graphing the trig functions, including sine and cosine graphs, and transformations
Inverse trig functions, including their graphs
Trig identities, including even-odd, sum-difference, half-angle, double-angle, product-to-sum, and sum-to-product identities
The law of sines and the law of cosines, including heron's formula

Polar curves, including converting coordinates and graphing polar curves
Complex numbers, including polar forms and de moivre's theorem
Matrices, including solving systems, gauss-jordan elimination, and transformations and inverses
Partial fractions, including fraction decomposition for all factor types
Conic sections and analytic geometry, including rotating conics and polar equations of conics
Parametric curves, including finding the direction of the parameter and the parametric representation
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Angles and their measure, including degrees, dms and radians
Six circular functions, including sine, cosine, tangent, cosecant, secant, and cotangent
The unit circle, including finding sine and cosine, and how to complete a triangle
Angles in circles, including oriented arcs, circular sectors, and linear and angular velocity
Graphing the trig functions, including sine and cosine graphs, and transformations
Inverse trig functions, including their graphs
Trig identities, including even-odd, sum-difference, half-angle, double-angle, product-to-sum, and sum-to-product identities
The law of sines and the law of cosines, including heron's formula
Polar curves, including converting coordinates and graphing polar curves
Complex numbers, including polar forms and de moivre's theorem
Matrices, including solving systems, gauss-jordan elimination, and transformations and inverses
Partial fractions, including fraction decomposition for all factor types
Conic sections and analytic geometry, including rotating conics and polar equations of conics
Parametric curves, including finding the direction of the parameter and the parametric representation
Show more
Show less

Syllabus

You thought you signed up to study triangles, but now your teacher is insisting you memorize a unit circle? Don’t worry, we’ve got some good tricks that make it much, much easier to remember.

What we'll learn in Trigonometry

How to get the most out of this course

Download the Trigonometry formula sheet

The EVERYTHING download

Learn about angles in standard position, relationships between angles, and how to convert angles from one set of units to another.

Introduction to angles

RESOURCE: Quiz solutions for this section

Naming angles

Complementary and supplementary angles

Positive and negative angles

Quadrant of the angle

Degrees, radians, and DMS

Coterminal angles

BONUS! Extra practice problems. :)

Explore the six circular functions: sine, cosine, tangent, cosecant, secant, and cotangent, and their relationships to one another.

Introduction to the six trig functions

Sine, cosine, and tangent

Cosecant, secant, cotangent, and the reciprocal identities

The quotient identities

The Pythagorean identities

Signs by quadrant

When the trig functions are undefined

Learn about the unit circle and how to use it to solve all kinds of problems with triangles and trig functions.

Introduction to the unit circle

The unit circle

Negative angles and angles more than one rotation

Coterminal angles in a particular interval

Reference angles

Symmetry across axes

Even-odd identities

The set of all possible angles

Points not on the unit circle

Solving right triangles

Angles of elevation and depression

Angles in circles

Introduction to angles in circles

Radians and arc length

Area of a circular sector

Trig functions of real numbers

Linear and angular velocity

Relating linear and angular velocity

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Introduces basic concepts in precise, approachable ways, which makes it ideal for beginners

Explores key concepts in angles and circular functions through interactive activities and clear explanations

Provides a comprehensive review of trigonometry and precalculus topics, making it suitable for learners with diverse backgrounds

Covers complex topics such as polar coordinates, complex numbers, and matrices, which are essential for advanced mathematics and engineering

Provides ample practice opportunities through quizzes and workbooks, which helps solidify understanding and prepare for assessments

Instructed by Krista King, an experienced educator known for making math accessible and enjoyable

Reviews summary

Trigonometry and precalculus mastery course

According to students, this trigonometry and precalculus mastery course is largely positive with one student praising the instructor, Krista King.

Instructor Krista King delivers superb courses.

"This is the fourth course by Krista King that I've completed and once again she's delivered a superb course."

The Analytic Geometry section could be improved.

"Only gripe, was that the section on Analytic Geometry felt, to be blunt, like it had been composed of stand alone videos and hodgepodged to fill a section."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Become a Trigonometry & Precalculus Master with these activities:

Review 'Algebra and Trigonometry' by Sullivan and Sullivan

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Review the textbook to reinforce your understanding of the concepts covered in this course.

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Read the chapters that correspond to the topics covered in the course.
Take notes on the important concepts.
Do the practice problems at the end of each chapter.
Review your notes before each class.
Use the textbook as a reference when you need help with the course material.

Watch Khan Academy Trig Tutorials

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Watch video tutorials to supplement your understanding of the course material.

Show steps

Go to the Khan Academy website.
Search for 'trigonometry'.
Watch the videos that correspond to the topics covered in the course.
Take notes on the important concepts.
Do the practice problems provided in the videos.

Review Unit Circle

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Review the unit circle to refresh your memory on the locations of the trigonometric function values.

Browse courses on Unit Circle

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Draw a unit circle.
Label the axes as sine and cosine.
Mark the points for 0, 30, 45, 60, 90, 120, 135, 150, 180, 210, 225, 240, 270, 300, 315, 330, and 360 degrees.
Draw radii from the origin to each of these points.
Determine the sine and cosine of each angle.

Five other activities

Expand to see all activities and additional details

Show all eight activities

Join a Study Group

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Join a study group to collaborate with other students and learn from each other.

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Find a study group that meets regularly.
Attend the study group meetings.
Participate in the discussions.
Help other students with their understanding of the material.
Learn from other students' perspectives.

Practice Trig Identities

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Practice using trigonometric identities to simplify expressions and solve equations.

Browse courses on Trigonometric Identities

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Find a list of trigonometric identities online or in a textbook.
Choose a few identities to practice.
Find practice problems that involve using these identities.
Solve the problems using the identities.
Check your answers.

Solve Trig Equations

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Practice solving trigonometric equations to improve your problem-solving skills.

Show steps

Find a list of practice problems online or in a textbook.
Choose a few problems to practice.
Solve the problems using the appropriate techniques.
Check your answers.
Review the solutions to see where you made mistakes.

Create a Trig Function Graph

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Create a graph of a trigonometric function to visualize its behavior and properties.

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Choose a trigonometric function to graph.
Determine the domain and range of the function.
Plot the key points of the function.
Sketch the graph of the function.
Label the graph with the important features.

Create a Trig Function Project

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Create a project that applies the concepts of trigonometry to a real-world problem.

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Choose a project topic.
Research the topic.
Develop a plan for the project.
Create the project.
Present the project to the class.

Career center

Learners who complete Become a Trigonometry & Precalculus Master will develop knowledge and skills that may be useful to these careers:

Mathematician

Mathematicians use their extensive mathematical knowledge to advance mathematical theories and solve complex problems in fields such as trigonometry. This course provides a foundation of trigonometry and precalculus knowledge that Mathematicians may find helpful for their work. The course covers angle measurements, trigonometric functions, identities, graphs, and more, all of which are essential concepts for Mathematicians to understand. By completing this course, learners can enhance their understanding of the fundamentals of trigonometry and precalculus, which can support their success in the field of Mathematics.

See salaries and explore the career path for Mathematician

Trigonometric Surveyor

Trigonometric Surveyors use trigonometry and surveying equipment to measure angles, distances, and elevations. This course can help build a foundation in trigonometry and precalculus that Trigonometric Surveyors can leverage in their work. The course covers topics such as angle measurements, trigonometric functions, identities, and graphing, all of which are essential for understanding the principles of trigonometry. By taking this course, learners can gain a deeper understanding of the mathematical concepts used in Trigonometric Surveying, enabling them to perform accurate and precise surveys.

See salaries and explore the career path for Trigonometric Surveyor

Astronomer

Astronomers use trigonometry and precalculus to calculate the positions, distances, and motions of celestial objects. This course provides a comprehensive foundation in trigonometry and precalculus that Astronomers may find useful for their work. The course covers angle measurements, trigonometric functions, identities, and graphs, as well as more advanced topics like polar coordinates, complex numbers, and matrices. By completing this course, learners can enhance their understanding of the mathematical principles used in Astronomy, which can support their success in the field.

See salaries and explore the career path for Astronomer

Robotics Engineer

Robotics Engineers use trigonometry and precalculus to design, build, and control robots. This course can help build a foundation in trigonometry and precalculus that Robotics Engineers can leverage in their work. The course covers topics such as angle measurements, trigonometric functions, identities, and graphing, all of which are essential for understanding the principles of trigonometry. By taking this course, learners can gain a deeper understanding of the mathematical concepts used in Robotics Engineering, enabling them to design and control robots more effectively.

See salaries and explore the career path for Robotics Engineer

Geodetic Engineer

Geodetic Engineers use trigonometry and precalculus to measure and analyze the Earth's shape and size. This course provides a foundation of trigonometry and precalculus knowledge that Geodetic Engineers may find helpful for their work. The course covers angle measurements, trigonometric functions, identities, and graphs, as well as more advanced topics like polar coordinates, complex numbers, and matrices. By completing this course, learners can enhance their understanding of the mathematical principles used in Geodetic Engineering, which can support their success in the field.

See salaries and explore the career path for Geodetic Engineer

Navigation Officer

Navigation Officers use trigonometry and precalculus to calculate the position and course of ships or aircraft. This course can help build a foundation in trigonometry and precalculus that Navigation Officers can leverage in their work. The course covers topics such as angle measurements, trigonometric functions, identities, and graphing, all of which are essential for understanding the principles of trigonometry. By taking this course, learners can gain a deeper understanding of the mathematical concepts used in Navigation, enabling them to perform accurate and precise navigation.

See salaries and explore the career path for Navigation Officer

Teacher

Teachers at elementary and secondary schools may teach trigonometry and precalculus to students. This course provides a foundation of trigonometry and precalculus knowledge that Teachers may find helpful for their work. The course covers angle measurements, trigonometric functions, identities, and graphs, as well as more advanced topics like polar coordinates, complex numbers, and matrices. By completing this course, learners can enhance their understanding of trigonometry and precalculus, which can support their success in teaching these concepts to students.

See salaries and explore the career path for Teacher

Engineer

Engineers use trigonometry and precalculus to design and build structures, machines, and systems. This course provides a foundation of trigonometry and precalculus knowledge that Engineers may find helpful for their work. The course covers angle measurements, trigonometric functions, identities, and graphs, as well as more advanced topics like polar coordinates, complex numbers, and matrices. By completing this course, learners can enhance their understanding of the mathematical principles used in Engineering, which can support their success in the field.

See salaries and explore the career path for Engineer

Computer Programmer

Computer Programmers use trigonometry and precalculus to develop software and applications. This course may provide a helpful introduction to trigonometry and precalculus that Computer Programmers can leverage in their work. The course covers topics such as angle measurements, trigonometric functions, identities, and graphing, as well as more advanced topics like polar coordinates, complex numbers, and matrices. By taking this course, learners can gain a deeper understanding of the mathematical concepts used in Computer Programming, enabling them to write more efficient and accurate code.

See salaries and explore the career path for Computer Programmer

Statistician

Statisticians use trigonometry and precalculus to analyze data and draw conclusions. This course may provide a helpful foundation in trigonometry and precalculus that Statisticians can leverage in their work. The course covers topics such as angle measurements, trigonometric functions, identities, and graphing, as well as more advanced topics like polar coordinates, complex numbers, and matrices. By taking this course, learners can gain a deeper understanding of the mathematical concepts used in Statistics, enabling them to analyze data more effectively and draw more accurate conclusions.

See salaries and explore the career path for Statistician

Operations Research Analyst

Operations Research Analysts use trigonometry and precalculus to solve complex problems in business and industry. This course may provide a helpful foundation in trigonometry and precalculus that Operations Research Analysts can leverage in their work. The course covers topics such as angle measurements, trigonometric functions, identities, and graphing, as well as more advanced topics like polar coordinates, complex numbers, and matrices. By taking this course, learners can gain a deeper understanding of the mathematical concepts used in Operations Research, enabling them to solve problems more effectively and efficiently.

See salaries and explore the career path for Operations Research Analyst

Actuary

Actuaries use trigonometry and precalculus to assess risk and uncertainty. This course may provide a helpful foundation in trigonometry and precalculus that Actuaries can leverage in their work. The course covers topics such as angle measurements, trigonometric functions, identities, and graphing, as well as more advanced topics like polar coordinates, complex numbers, and matrices. By taking this course, learners can gain a deeper understanding of the mathematical concepts used in Actuarial Science, enabling them to assess risk and uncertainty more accurately.

See salaries and explore the career path for Actuary

Financial Analyst

Financial Analysts use trigonometry and precalculus to analyze financial data and make investment decisions. This course may provide a helpful foundation in trigonometry and precalculus that Financial Analysts can leverage in their work. The course covers topics such as angle measurements, trigonometric functions, identities, and graphing, as well as more advanced topics like polar coordinates, complex numbers, and matrices. By taking this course, learners can gain a deeper understanding of the mathematical concepts used in Financial Analysis, enabling them to analyze financial data more effectively and make better investment decisions.

See salaries and explore the career path for Financial Analyst

Data Scientist

Data Scientists use trigonometry and precalculus to analyze and interpret data. This course may provide a helpful foundation in trigonometry and precalculus that Data Scientists can leverage in their work. The course covers topics such as angle measurements, trigonometric functions, identities, and graphing, as well as more advanced topics like polar coordinates, complex numbers, and matrices. By taking this course, learners can gain a deeper understanding of the mathematical concepts used in Data Science, enabling them to analyze and interpret data more effectively.

See salaries and explore the career path for Data Scientist

Software Engineer

Software Engineers use trigonometry and precalculus to design and develop software applications. This course may provide a helpful foundation in trigonometry and precalculus that Software Engineers can leverage in their work. The course covers topics such as angle measurements, trigonometric functions, identities, and graphing, as well as more advanced topics like polar coordinates, complex numbers, and matrices. By taking this course, learners can gain a deeper understanding of the mathematical concepts used in Software Engineering, enabling them to design and develop more efficient and reliable software applications.

See salaries and explore the career path for Software Engineer