Trigonometry: Pythagorean Trigonometric Identity
This is a free lesson from our course in Trigonometry
 
   
This lesson introduces the concept of Pythagorean trigonometric identities. The instructor will explain it to you in his/her own voice and handwriting in the video with some examples that will help you to understand the concepts and to improve your study skills.
The Pythagorean trigonometric identity is a trigonometric identity expressing the Pythagorean Theorem in terms of trigonometric functions. Along with the sum-of-angles formulae, it is the basic relation among the sin and cos functions from which all others may be derived. For example: let's look at the relationship between one of the important identity sin2  + cos2  = 1 and the Pythagorean Theorem. (More text below video...)
<h2>Trigonometry - Pythagorean Trigonometric Identity</h2> <p>Trigonometric identities, example, trigonometry, video, functions, sine, cosine, tangent, cotangent, secant, simplifying, cosecant, Pythagorean Theorem, verifying identity, right triangle, legs, hypotenuse, practice question, quizzes, solution, lesson, trigonometry help</p> <p>A trigonometric identity is different from a trigonometric expression in that an identity will have an equal (=) sign in it. There are many ways to go about justifying identities, but a few are used often.</p>
Other useful lessons:
Verifying Trigonometric Identities
Getting started - Trigonometric identities
(Continued from above) The Pythagorean Theorem states that if the legs of a right triangle are a and b, and hypotenuse is c, then
(Hypotenuse)2 = (Adjacent)2 + (Opposite)2   i.e., c2 = a2 + b2.
In a right triangle, x and y are the legs, hypotenuse r, and be the measure of the central angle. Then the values of the six trigonometric functions are given by:
  sin = opposite/hypotenuse =  y/r,
  cos  = adjacent/ hypotenuse = x/r, 
  tan  = opposite/adjacent = y/x, 
  csc  = hypotenuse/opposite = r/y, 
  sec  = hypotenuse/adjacent = r/x,
  cot  = adjacent/opposite = x/y.
You'll also learn the proof of identity sin2  + cos2  = 1.
Two more Pythagorean Identities are:
  tan2 + 1 =sec2
  cot2 + 1 = csc2
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