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What is Trigonometry
Trigonometry is a branch of mathematics that deals with angles and sides of triangles, especially right-angled triangles. The three main trigonometric functions include sine, cosine, and tangent. These trigonometric functions are the basics of trigonometry.
Sine function is the ratio of the length of the hypotenuse of a right-angled triangle. Cosine is the ratio of the length of the adjacent side of the hypotenuse. Tangent is the ratio of the opposite side’s length to the adjacent side’s length. These basic identities will help to know how to learn trigonometry.
The topic can be classified into three different sections which involve Core trigonometry (right-angled triangles), plane trigonometry (all types of 2-dimensional geometry), and Spherical trigonometry (all types of 3-dimensional geometry). These classifications are included in advanced learning trigonometry.
There are more trigonometric ratios or identities apart from sine, cosine, and tangent. They are sec, cosec, and cotangent. These identities are related to each other from multiple different angles.
Looking to Learn Trigonometry? Book a Free Trial Lesson and match with top Trigonometry Tutors for Concepts, Homework Help, and Test Prep.
Trigonometric Formulas
If you know the trigonometric formulas, the trigonometry table is very easy to remember for complex numbers. Below we are giving some simple formulas(for right-angled triangles) to find out trigonometric function.
Ratios
- sine = (opposite side) / hypotenuse
- cosine = (adjacent side) / hypotenuse
- tangent = (opposite side) / (adjacent side)
Reciprocals
- 1/sin x = cosec x
- 1/cos x = sec x
- 1/tan x = cot x
Fundamental unique properties
- sin2θ + cos2θ = 1
- 1 + tan2θ = sec2θ
- 1 + cot2θ = cosec2 θ
Best ways to understand Trigonometry
How to understand trigonometry can be figured out easily with the right resources. There are several online ways to help you start your trigonometry learning journey or encourage your knowledge of trigonometric values. Some of them are:
- Trigonometry tutoring services
- Trigonometry online courses
- Trigonometry worksheets
- Trigonometry online games
Trigonometry tutoring services
Wiingy
Wiingy is a top-rated tutoring platform offering private lessons to students of all ages. Thousands of students use Wiingy for conceptual mathematical understanding, homework help, and test prep. Students and parents consistently rate the Wiingy experience as 4.8 out of 5.
Wiingy has a rigorous tutor selection process, which includes screening, interviews, and assessments. Less than 3% of applicants qualify to be a tutor on the Wiingy platform. So, you work only with highly qualified, experienced, and verified trigonometry tutors.
Mathnasium
Mathnasium offers online and in-person tutoring services to K-12 students, focusing only on math subjects like trigonometry, geometry, algebra, and calculus.
Upon signing up, you need to complete a brief math skills evaluation followed by a telephonic assessment to identify your academic goals and learning preferences. This helps match you with the best trigonometry tutor for your needs.
Superprof
Superprof is another leading online tutoring marketplace that connects students with trigonometry tutors from all over the world. It offers both online and in-person tutoring services.
The platform ensures you learn trigonometry at your own pace with a personalized teaching approach according to the curriculum. You can visit any trigonometry teacher’s profile as per your learning needs and click the ‘Book a Class’ button to proceed with your first lesson.
At Superprof, you get to choose from a large pool of tutors and connect with the right one.
Trigonometry online courses
Coursera
Coursera offers high-in-class, well-organized trigonometry courses through partnerships with prominent academic institutions (Yale University, University of Michigan, and more) and businesses (Google, Goldman Sachs, and more).
The modules reflect thorough information on the subject matter in comprehensible language for all levels of trigonometry. Earning credentials from Coursera can also improve your resume.
Class Central
It offers you access to a wide variety of free and paid online courses from top universities and educational platforms. With user reviews and ratings, you can easily find high-quality courses that have helped others master trigonometry.
Additionally, Class Central provides detailed course descriptions and syllabi, helping you understand trigonometry. It does not depend on whether you’re a beginner or looking to deepen your understanding.
Udemy
Udemy is an online marketplace for learning and teaching with over 1,55,000 courses and 40 million students. It has a vast range of courses for trigonometry coupled with algebra courses. These courses are designed to help all levels of trigonometry learners, also to prepare for their college exams or simply to refresh their knowledge of trigonometry.
Udemy trigonometry courses give you online access to subject learning with engaging video lessons and interactive exercises.
Trigonometry Worksheets
Math Worksheets 4 Kids
It provides a surplus collection of trigonometry worksheets that cover key skills in quadrants and angles measuring angles in degrees. It offers online and printable worksheets with attractive fonts and diagrams. Some sample worksheets are also available to help you understand the type of questions.
These worksheets include topics like radians, conversion between degrees, understanding the six trigonometric ratios, unit circles, and more.
Math-Aids.com
It offers free trigonometry worksheets to tutors, parents, students, and homeschoolers. You can select different variables to customize the worksheets as per your preference. These are free to download, printable, and easy to use.
Math-Aids.com refreshes its trigonometry worksheets every day. Therefore, it has endless provision of new worksheets. These trigonometry Worksheets are helpful for children in grades 5, 6, 7, and 8.
EdHelper.com
It offers thorough and detailed trigonometry worksheets intending to build a solid foundation in students. These worksheets are based on the Law of Sines, the Law of Cosines, tangents, and other trigonometric functions.
These worksheets are tailored by the trigonometry teachers catering to all types of trigonometry learners. The website also contains workbooks, puzzles, and thought-provoking riddles.
Trigonometry online games
PhET
The website is designed for online math games catering to all types of trigonometry learners. It follows the Common Core Standard of math. The games display captivating characters and interesting visuals to keep children excited throughout the learning process.
Multiple games cover topics like pythagorean theorem, unit circle scales, tangent line, standard angles, similar triangles, sines, and cosines. You can estimate the value of trigonometry functions for any given angle without a calculator using the unit circle concept.
Purpose Games
Purpose Games combines interactive learning, visual aids, immediate feedback, and games to create an effective and engaging platform for understanding trigonometry.
Tutors and fellow students create many trigonometry quizzes and games. It provides a diverse range of perspectives and ways to understand visualize relationships present in triangles.
OnlineLearningMath.com
The website features interactive tools such as quizzes, practice problems, and visual aids like graphs and diagrams that enhance understanding and retention of trigonometry concepts.
The website includes additional resources such as worksheets, reference materials, and links to other helpful educational websites, providing a well-rounded learning experience.
Why learn Trigonometry
We learn trigonometry because it has multiple uses in our daily lives. For example, in geography, we measure the distance between landmarks using trigonometric functions. In space, we use trigonometric identities to measure distance between starts and satellites, when we cannot measure manually.
Trigonometry is used to represent sound waves in mathematical terms. Sound engineers and technologists who research deeply in computer music and even in hi-tech music have to relate to the basic laws of trigonometry.
Another real-life application of trigonometry is digital imaging or animations. Geometric patterns are used in computer-generated images and if they are referred to as a triangle terminology, trigonometric identities, and ratios are applied to give the result.
If you are interested in trekking, you must know how the height of the huge mountains is determined. Base, length, and hypotenuse from the sea level which are trigonometric identities confirm the height and other features of tall structures.
Looking to Learn Trigonometry? Book a Free Trial Lesson and match with top Trigonometry Tutors for Concepts, Homework Help, and Test Prep.
Conclusion
Understanding trigonometry is achievable with the right approach by staying focused on your goal. Start with the basic trigonometric concepts, practice regularly, use interactive tools and resources, and do not hesitate to seek help when needed. With dedication and right strategies, you will be able to solve trigonometry with ease.
Other useful resources
Frequently Asked Questions
What grade do you learn trigonometry?
Trigonometry is generally introduced in the US in high school, in 10th grade. Also, this can vary depending on the school and its mathematics curriculum.
Trigonometry often combines with geometry or algebra curriculum in 8th and 9th grade. However, a more depth understanding of the subject is taken up in high school.
Is trigonometry hard?
For many students, trigonometry can be challenging initially, but it becomes more manageable with consistent effort, practice, and possibly additional help from a trigonometry tutor.
If you have a strong base of percentages, algebra, and geometry, learning trigonometry would be easy as it relates trigonometric functions, like sine and cosine to them.
How can a beginner learn trigonometry?
A beginner can learn trigonometry by starting with the basics of angles and triangles, particularly right-angled triangles. It’s important to understand the sine, cosine, and tangent trigonometric functions, which relate the angles of a triangle to the lengths of its sides.
Additionally, seeking help from a teacher or tutor can provide personalized assistance and clarification of difficult concepts.
How long does it take to learn trigonometry?
The time it takes to learn trigonometry varies depending on the individual’s prior math knowledge, learning pace, and study methods. For a high school student, a typical trigonometry chapter might span several weeks to a few months within a math course.
For a dedicated learner, spending a few hours a week studying trigonometry concepts, practicing problems, and seeking help as needed, it could take anywhere from a few weeks to a few months to gain a solid understanding. Consistent practice and review are key to mastering the subject.
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Medha PandeyReviewed by by
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