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Solving Trigonometric Equations 3715 Views


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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.

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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

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