What is Trigonometry?
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Introduction to Trigonometry
When you start any new class, it’s always a good idea to have a basic understanding of the subject before diving into the details. This is especially true when it comes to more advanced math and science courses. You’ll move from subjects like algebra and geometry to more complex topics like trigonometry and calculus.
Today, we’re focusing on trigonometry. By the end of this blog, you’ll be able to answer the question “What is trigonometry?” and you’ll have a solid understanding of its core principles to help you approach it with confidence.
What is the Definition of Trigonometry?
Let’s keep it simple. Trigonometry is “a branch of mathematics that deals with the relationships between the sides and angles of triangles.”
In simpler terms, trigonometry is a type of math that helps us understand how the sides and angles of triangles are connected. It’s all about triangles—specifically, right triangles. Trigonometry introduces new tools called sine, cosine, and tangent, which are essential for solving problems with angles and distances.
Key Elements of Trigonometry: Sine, Cosine, and Tangent
Trigonometry is built on three major functions that help us calculate unknown sides and angles of triangles. Here’s a breakdown of each one.
What is Sine?
The sine function (abbreviated as sin) compares the length of the opposite side to the hypotenuse of a right triangle.
Formula: Sin(θ) = Opposite / Hypotenuse
Example Use: If you know an angle and the hypotenuse, you can use sine to find the length of the opposite side.
What is Cosine?
The cosine function (abbreviated as cos) compares the length of the adjacent side to the hypotenuse of a right triangle.
Formula: Cos(θ) = Adjacent / Hypotenuse
Example Use: If you know an angle and the hypotenuse, you can use cosine to find the length of the adjacent side.
What is Tangent?
The tangent function (abbreviated as tan) compares the length of the opposite side to the adjacent side of a right triangle.
Formula: Tan(θ) = Opposite / Adjacent
Example Use: If you know an angle and one side of a triangle, tangent can help you find the other side.
Study Tip! Remember SOH-CAH-TOA
A popular study method for easily remembering your trigonometric ratios is called SOH-CAH-TOA.
SOH: Sine is Opposite over Hypotenuse
CAH: Cosine is Adjacent over Hypotenuse
TOA: Tangent is Opposite over Adjacent
"Opposite" refers to the side length the angle faces, "adjacent" refers to the side length next to the angle, and "hypotenuse" refers to the longest side length, opposite to the right angle. These three functions—sine, cosine, and tangent—are the building blocks of trigonometry. Want to learn more about how they work? Check out our guide All About Trigonometric Ratios for a deeper dive.
Why Do We Need Trigonometry?
Trigonometry isn’t just about triangles in a textbook—it’s all around you in the real world. Here are some career paths that utilize trigonometry on a daily basis:
Engineering and Construction: Building bridges, skyscrapers, and roads all require trigonometry to calculate angles and measurements.
Astronomy and Space Exploration: Measuring the distance between planets and stars wouldn’t be possible without trigonometry.
Navigation and GPS: Modern GPS systems rely on trigonometry to determine locations and distances.
Video Game Design: Creating 3D graphics and animations in video games requires the use of trigonometry to make characters and objects move in realistic ways.
Sign Up with UPchieve for Trigonometry Help
Now that you know the answer to “What is trigonometry?” and have a better understanding of sine, cosine, and tangent, you’re ready to start tackling this subject with confidence. These concepts are essential for solving problems with triangles and will help you in future classes like calculus and physics.
Still have questions about trigonometry or need help with a tricky concept? Whether it’s understanding angles, solving equations, or applying trigonometric functions, UPchieve’s tutors are here to support you. Connect with a tutor anytime—it’s as easy as calculating the hypotenuse of a right triangle!
Prefer to keep learning on your own? Check out our other math resources on geometry, algebra, and quadratic equations. And don’t forget to visit UPchieve.org or download the UPchieve app for free, on-the-go homework help whenever you need it—in as little as five minutes!
UPchieve FAQ: Common Questions About Trigonometry Support
How much does a trigonometry tutor cost?
At UPchieve, trigonometry tutoring is completely free as part of our nonprofit mission to help students from low-income backgrounds. UPchieve’s tutoring is free thanks to generous donations from people and organizations who want to make tutoring accessible to everyone.
Can I find a trigonometry tutor near me?
With UPchieve, you don’t need to search for “trigonometry tutors near me.” Our online platform connects you with expert trigonometry tutors from anywhere in the U.S. where you’ll get personalized online support from one of our tutors.
Is your online trigonometry tutoring flexible?
Yes! Our online tutoring allows you to connect with expert tutors anytime you need help—day, night, or whenever you’re ready to study.
What topics do your trigonometry tutors cover?
UPchieve’s certified tutors can help with any topic you’ll encounter in a high school trigonometry class, including sine, cosine, tangent, trigonometric identities, and graphing trigonometric functions.
How do I know if I need a trigonometry tutor?
Here are some signs you might need extra support:
You’re struggling with problem-solving or logic.
You’re falling behind on homework.
Your grades are declining despite your efforts.
Your teacher’s explanations don’t make sense.
A tutor can help you overcome these challenges and build the confidence to succeed.
Can trigonometry tutoring help with test preparation?
Yes! Our tutors can help you prepare for standardized tests like the SAT, ACT, and AP exams. We’ll guide you through common exam questions, teach you test-taking strategies, and help you practice problem-solving.
Why should I choose online trigonometry tutoring?
Online tutoring is flexible and accessible. Study from home, the library, or anywhere with an internet connection. Plus, you’ll have access to expert tutors who can help when it’s convenient for you.
Can I get help with trigonometry homework?
Absolutely! UPchieve’s tutors will guide you through tough homework questions and help you understand the concepts, so you can solve similar problems on your own.
How can I sign up for free trigonometry tutoring?
Sign up for a free UPchieve account, connect with a tutor in under 5-10 minutes, and use the chat and virtual whiteboard to get help with trigonometry. It’s that simple!