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 sumofangles 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 sin^{2}
+ cos^{2}
= 1 and the Pythagorean Theorem. (More text below video...)
(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., c^{2} = a^{2} + b^{2}.
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 sin^{2}
+ cos^{2}
= 1.
Two more Pythagorean Identities are:
tan^{2}
+ 1 =sec^{2}
cot^{2}
+ 1 = csc^{2}
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