ShmoopTube

Where Monty Python meets your 10th grade teacher.

Search Thousands of Shmoop Videos


Precalculus Videos 6 videos

ACT Math 3.1 Coordinate Geometry
501 Views

ACT Math: Coordinate Geometry Drill 3, Problem 1. What shape is shown by the equation in this video?

ACT Math 4.3 Elementary Algebra
346 Views

ACT Math Elementary Algebra Drill 4, Problem 3. Simplify the expression.

See All

Verifying Trig Identities 1729 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.

Language:
English Language

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]

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

Solving Trigonometric Equations
3719 Views

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.

Surface Area of Cylinders
14741 Views

Haven't you always wondered how much cardboard it takes to encase a trunk warmer for your pet elephant?

Perimeter of Irregular Shapes
4864 Views

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...

Introduction to 3D Geometry
55503 Views

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...

An Introduction to 3D Geometry
815 Views

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...