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Pythagorean Identities - Examples & Practice Problems, Trigonometry
This trigonometry video tutorial provides a basic introduction into the Pythagorean identities of trigonometric functions. it provides plenty of examples and practice problems of evaluating cosine given the value of sine.
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Video Transcript
now let's talk about the pythagorean
identities
there's three of them that you need to
be aware of the first one is the most
common
sine squared
of theta
plus
cosine squared theta is equal to one
that's the first one
here are the other two one plus tangent
squared
is equal to secant squared
and 1 plus cotangent squared
is equal to cosecant squared so those
are the pythagorean identities but let's
focus on the first one and how we can
use it
so let's say sine theta
is equal to 4 over 5.
and let's say the angle theta
is between 0 and 90.
using this information and this is in
degrees by the way
what is the value of cosine theta
how can we find the value of cosine
so using the pythagorean
identity sine squared plus cosine
squared is one
if we know the value of sine we could
find the value of cosine
sine is four over five
so now let's calculate the value of
cosine
four squared is sixteen five squared is
twenty five
and one
we can write it as twenty five divided
by twenty five
now the next thing that we could do
is we could subtract both sides by 16
over 25
so cosine squared theta is 25 over 25
minus 16 over 25
25 minus 16 is 9
so we have 9 over 25
and now we need to take the square root
of both sides
the square root of 9 is 3
the square root of 25 is 5.
