ShmoopTube
Where Monty Python meets your 10th grade teacher.
Search Thousands of Shmoop Videos
Precalculus Videos 6 videos
ACT Math: Coordinate Geometry Drill 3, Problem 1. What shape is shown by the equation in this video?
ACT Math Elementary Algebra Drill 4, Problem 3. Simplify the expression.
Verifying Trig Identities 1730 Views
Share It!
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
Related Videos
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.
Haven't you always wondered how much cardboard it takes to encase a trunk warmer for your pet elephant?
Want to figure out the area and perimeter of irregular shapes? Break them down into regular shapes. For example, a flower can be broken down into s...
It's one thing when all those shapes are sitting flat on the page. But when they start popping out and invading our personal space bubble, we get a...
Does thinking about 3D Geometry get you bent out of shape? Never fear! Watch this video and figure out some fun new shapes to bend back into. We're...