Trigonometry: Definitions of Trigonometric Functions
This is a free lesson from our course in Trigonometry
 
   
In this lesson, you'll learn how to relate the angles and sides of a right triangle. It is followed by explanation of the trigonometric functions. This is done with the help of several examples, video and explanation by instructor in own hand writing. It includes the practice questions with solutions to help solving math problems.
In a right angle triangle, for angle , the name of the sides is:
  • Hypotenuse (the side opposite the right angle)
  • Adjacent (the side "next to" )
  • Opposite (the side farthest from the angle)
(More text below video...)
<h2>Trigonometry - Definitions of Trigonometric Functions</h2> <p>trigonometric identities, basic, trigonometric functions, video, Pythagorean Identities, sine, cosine, tangent, explanation, example, cotangent, secant, cosecant, trigonometry, value, variables, solution, identities, practice questions, quizzes, Pythagorean</p> <p>The trigonometric identities are equalities that involve trigonometric functions that are true for every single value of the occurring variables</p>
Other useful lessons:
The unit circle, Sine, and Cosine
Graphs of Sine
(Continued from above) The trigonometric ratios sine , cosine , and tangent q (in short form- sin , cos , and tan ) are defined as:
     sin  = opposite/hypotenuse
     cos  = adjacent/hypotenuse
     tan  = opposite/adjacent
To help you remember the important facts, you can use SOH CAH TOA.
SOH stands for Sine equals Opposite over Hypotenuse i.e., 
     sin  = opposite/hypotenuse,
CAH stands for Cosine equals Adjacent over Hypotenuse i.e., 
     cos = adjacent/hypotenuse
TOA stands for Tangent equals Opposite over Adjacent i.e., 
     tan  = opposite/adjacent,
where  represents an angle.
Trigonometric functions are defined as ratios of the sides of a right triangle (sine, cosine, tangent, cotangent, secant, and co secant), and can equivalently be defined as the lengths of various line segments from a unit circle. More modern definitions express them as infinite series or as solutions of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers.
The reciprocal functions of sine, cosine and tangent are cosecant, secant and cotangent respectively. They are generally written as csc, sec and cot. For any angle , these   functions can be expressed as
     csc  = 1/sin 
     sec  = 1/cos  
     cot  = 1/tan
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