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Linear and Nonlinear Equations Videos 15 videos
SAT Math 1.3 Algebra and Functions. How many 16 oz. bottles did she buy?
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.
Solving Trigonometric Equations 3717 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.
- Functions / Extend the domain of trigonometric functions using the unit circle
- Functions / Model periodic phenomena with trigonometric functions
- Functions / Prove and apply trigonometric identities
- Geometry / Similarity, right triangles, trigonometry, and dimensions
- Geometry / Define trigonometric ratios and solve problems involving right triangles
- Functions / Extend the domain of trigonometric functions using the unit circle
- Functions / Model periodic phenomena with trigonometric functions
- Functions / Prove and apply trigonometric identities
- Similarity, Right Triangles, and Trigonometry / Define trigonometric ratios and solve right triangle problems
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
Full Transcript
- 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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