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...)
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 Winpossible's online math courses and tutorials have gained rapidly popularity since their launch in 2008. Over 100,000 students have benefited from Winpossible's courses... these courses in conjunction with free unlimited homework help serve as a very effective math-tutor for our students.
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