Trigonometry: A Trig Cheat Sheet for Solving Problems

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It has various applications in fields like physics, engineering, and navigation. Understanding trigonometry can be challenging, but having a "Trig Cheat Sheet" can make it much easier.

Here is a quick overview of the basic concepts in trigonometry:

Right-Angled Triangles

A right-angled triangle has one angle that measures 90 degrees. The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs. The trigonometric functions are defined in terms of the ratios of the sides of the triangle.

The three primary trigonometric functions are:

  • Sine (sin): the ratio of the length of the side opposite the angle to the length of the hypotenuse.
  • Cosine (cos): the ratio of the length of the adjacent side to the length of the hypotenuse.
  • Tangent (tan): the ratio of the length of the side opposite the angle to the length of the adjacent side.

Trigonometric Identities

Trigonometric identities are equations that are true for all values of the variables. Some important trigonometric identities are:

  • Pythagorean Identity: sin²(θ) + cos²(θ) = 1
  • Reciprocal Identities: sin(θ) = 1/csc(θ), cos(θ) = 1/sec(θ), tan(θ) = 1/cot(θ)
  • Even/Odd Identities: sin(-θ) = -sin(θ), cos(-θ) = cos(θ), tan(-θ) = -tan(θ)

Trigonometric Formulas

Trigonometric formulas are useful for solving problems involving angles and sides of triangles. Some important formulas are:

  • Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
  • Law of Cosines: c² = a² + b² - 2ab cos(C)
  • Double Angle Formulas: sin(2θ) = 2sin(θ)cos(θ), cos(2θ) = cos²(θ) - sin²(θ), tan(2θ) = (2tan(θ))/(1-tan²(θ))

Trigonometric Graphs

Trigonometric functions can be represented graphically. The sine and cosine functions have a periodic nature and repeat their values after every 2π radians (or 360 degrees). The tangent function has vertical asymptotes at odd multiples of π/2.


Trigonometry is an important branch of mathematics with many applications in different fields. A "Trig Cheat Sheet" can be a valuable tool for understanding the basic concepts, identities, formulas, and graphs of trigonometry. With practice, you can become proficient in solving trigonometric problems and develop a deeper understanding of the subject.

So, if you want to master trigonometry, start by memorizing this Trig Cheat Sheet and use it as a reference whenever you need to solve trigonometric problems.
Table of Contents

  • Right triangle definition
  • Facts and Properties
  • Formulas and Identities
  • Inverse Trig Functions
  • Law of Sines, Cosines and Tange

In this tutorial on trigonometry, we'll cover the basics of right triangles and the primary trigonometric functions, as well as important formulas and identities that will help you solve problems involving angles and sides of triangles. We'll also explore the inverse trig functions and the Law of Sines, Cosines, and Tangents. Throughout the tutorial, we'll refer to a "Trig Cheat Sheet" to help you quickly recall key concepts and formulas. By the end of this tutorial, you'll have a solid understanding of trigonometry and be equipped with the tools you need to excel in this important branch of mathematics.

Size : 183.778 Kb
File type : pdf
Downloads: 11
Created: 2023-04-16
Trigonometry: A Trig Cheat Sheet for Solving Problems

Others Trig Cheat Sheet Tutorials

Others related eBooks about Trigonometry: A Trig Cheat Sheet for Solving Problems

Foundations of Software Science and Computation Structures

Download free course Foundations of Software Science and Computation Structures, pdf file on 556 pages by Miko?aj Boja?czyk, Alex Simpson....

Principles of Management

This book teaches management principles to tomorrow's business leaders by weaving three threads through every chapter: strategy, entrepreneurship and active leadership. ...

Internet of Things (IoT) in 5 Days: an easy guide to Wireless Sensor Networks (WSN), IPv6, and IoT

This booklet is a quick but thoughtful guide to jump into the Internet of Things (IoT), covering important subjects as IPv6 networking, sensors, wireless protocols and technologies, as well as IoT cloud platforms and its most commonly used protocols, featuring lots of hands-on examples to start work...

Artificial Intelligence: Foundations of Computational Agents, 2nd Edition

This text is a modern and coherent introduction to the field of Artificial Intelligence that uses rational computational agents and logic as unifying threads in this vast field. Many fully worked out examples, a good collection of paper-and-pencil exercises at various levels of difficulty, programmi...

Complete guide to Adobe Photoshop

With this pdf tutorial you will be able to create your own project in Photoshop .You will learn all the basics and create a project from scratch. Free training courses designated for student....

Don't Panic: Mobile Developer's Guide to The Galaxy

Download free course Don't Panic: Mobile Developer's Guide to The Galaxy, pdf file on 337 pages by Marco Tabor, Mladenka Vrdoljak....

Elixir Succinctly

Download free course Elixir Succinctly, pdf file on 84 pages by Emanuele DelBono....

A Graduate Course in Applied Cryptography

Cryptography is an indispensable tool used to protect information in computing systems. It..., download free Cryptography tutorial in PDF (900 pages) created by Dan Boneh ....

Advances in Flight Control Systems

Nonlinear problems in flight control have stimulated cooperation among engineers and scientists from a range of disciplines. Developments in computer technology allowed for numerical solutions of nonlinear control problems, while industrial recognition and applications of nonlinear mathematical mo...

RavenDB in Action

Download free course RavenDB in Action, pdf file on 221 pages by Itamar Syn-Hershko....