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.

Conclusion

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.

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Created: 2023-04-16
Trigonometry: A Trig Cheat Sheet for Solving Problems

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