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

Solving Trigonometric Equations 3719 Views


Share It!


Description:

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.

Language:
English Language

Transcript

00:00

Thank you We sneak in solving trigonometry equations Allah shmoop

00:08

calico is in a precarious situation She naively volunteered to

00:12

sit in the dunking booth at a carnival Helped raise

00:14

money for the vet club at school Calico is doomed

00:17

to her kool aid dunk If the next person in

00:20

line doesn't quickly and correctly solve the following trigon a

00:23

metric equations tangent squared of x minus three equals zero

00:29

For the interval zero is less than are equal to

00:32

x is less than or equal to to pi As

00:36

fate would have it speed of the slowest dog in

00:38

town is in line to try to solve her question

00:40

he grabs the marker and begin solving the equation by

00:43

factoring the expression If we factor the expression tangents squared

00:47

of x minus three like the difference of two squares

00:50

will have the expression the quantity tangent of x minus

00:54

square root of three times the quantity tangent of ax

00:56

plus square root of three In a bold move he

00:59

is now setting each of the quantities equal to zero

01:02

He knows that if their product together is zero then

01:05

one or both of them must be equal to zero

01:08

Solving each of the equations with a speed we frankly

01:10

didn't think possible for him He ends up with two

01:13

equations using a technique he must have studied with his

01:17

trigonometry teacher He is taking the inverse tangent of both

01:21

of the equations to solve for x reaching far back

01:24

into the recesses of his canine brain He recalls that

01:27

the inverse tangent of route three is pi over three

01:31

And the inverse tangent of negative Ruth 3 is 2

01:34

pi over three Speedy realizes that we've found two answers

01:38

within an interval of pie because both pie over three

01:42

and two pi over three are less than pie That

01:45

makes sense because the tangent function has a period of

01:48

pi which means it goes through one full cycle for

01:50

every pie radiance Since speedy is looking for all answered

01:54

between zero and two pie he has to consider the

01:57

answer's between pi and two pi Also in order to

02:00

find those values he needs tto add pie each of

02:03

the answers he already has So who had pi tau

02:07

pi over three We must first make sure both numbers

02:10

have the same denominator We can multiply three over three

02:13

And a pie to make it have the common denominator

02:16

of three When adding fractions we add across the top

02:20

and keep the denominator the same so three pi over

02:23

three plus pie over three equals four pi over three

02:28

brad pie to two pi over three We again have

02:31

to make sure both numbers are under the same denominator

02:34

we can again multiply three over three two pie to

02:36

get three pi over three plus two by over three

02:39

adding across the top Numbers we get 3 pie plus

02:43

two pi equals five pie over three Those final answers

02:48

are x equals pi over three four pi over three

02:53

two pi over three and five pie over three Unbelievable

02:57

speedy has solved the trig equation Unfortunately the dunk tank

03:02

malfunctions and calico gets drenched anyway Sh

Related Videos

Solving Systems of Linear Inequalities
11432 Views

How do you solve a system of linear inequalities? Aw, man...and we thought solving a problem like Maria was tough...

Solving Systems of Linear Equations in Three Variables
823 Views

Please note: If starting your own petting zoo, Shmoop recommends you stock it with animals that aren’t quite so likely to bite your hand off. Tha...

Solving Systems of Equations by Substitution
14328 Views

We just love us some alliteration.

Solving Systems of Equations by Elimination
8202 Views

Solving systems of equations by elimination: Survivor-style. Sorry, y... the tribe as spoken.

ACT Math 3.4 Intermediate Algebra
641 Views

ACT Math: Intermediate Algebra Drill 3, Problem 4. Solve this system.