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Verifying Trig Identities 1729 Views
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Description:
Verifying trig identities is important, especially when you're about to let one of them into the country—which is why they should keep their passports on them at all times.
Transcript
- 00:00
verifying trig identities a la shmoop. hemlock Jones has been competing for
- 00:09
respect as a detective all of which adult life but he is always outshined by [Jones in town square]
- 00:14
that pesky Sherlock Holmes if only there was a larger problem I could solve then [Jones in victorian apartment]
- 00:21
I could get the key to the city Jones Jones we've got to solve this riddle the
- 00:26
save candy looks different tis true but actually the same proved [Wilson walks in]
Full Transcript
- 00:32
their equality or it's over for your Dame cosine X plus sin x times tangent
- 00:39
X what do you make of it sounds like nonsense to me we must share that the
- 00:49
sum of cosine X and sine X you verify this trig identity we will substitute [Jones at chalkboard]
- 00:59
other known trig identities until we have equal sides to all equation we can
- 01:06
substitute sine x over cosine X for tangent X when we multiply sine X by
- 01:12
sine x over cosine X we get that cosine of X plus the fraction sine x over
- 01:20
cosine x sine x equals secant X what is it when we take in value times itself
- 01:30
squared Oh precisely my boy since we have the product of sines in the second
- 01:36
term we can simplify to cosine of X plus the fraction sine squared of X divided
- 01:43
by cosine of X equals secant X now what do I do we know the cosine squared X
- 01:52
plus sine squared X equals 1 how could I get 2 cosine squared X plus sine squared [math book]
- 01:58
X equals 1 on the left hand side oh I know we can multiply the left-hand [Jones on victorian couch]
- 02:03
side by the fraction cosine x over cosine X we get cosine squared of X [chalk board]
- 02:09
divided by cosine of X plus the fraction cosine X over cosine X times sine
- 02:15
squared X over cosine x equals secant X since cosine x over cosine X is just a
- 02:23
fancy way to write one we really just multiplying left side by one wrong if we
- 02:28
simplify the crazy left hand side we get cosine squared of X plus sine squared of
- 02:32
x over cosine of x equals secant of X cosine squared plus sine squared equals
- 02:37
one so we get 1 divided by cosine X equals secant X and the definition of [math book]
- 02:44
secant of X is 1 divided by the cosine of X so we have small problem
- 02:49
later that day candy is back in hemlocks on my hero [Jones and Candy on the couch]
- 02:53
oh it was nothing my dear I'm always looking out for any victim of
Up Next
FYI: cats don't like to get wet. Okay, so that fact won't be relevant every time you solve trig equations, but it happens to be this time.
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