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Thank you We sneak in solving trigonometry equations Allah shmoop

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calico is in a precarious situation She naively volunteered to

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sit in the dunking booth at a carnival Helped raise

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money for the vet club at school Calico is doomed

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to her kool aid dunk If the next person in

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

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metric equations tangent squared of x minus three equals zero

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For the interval zero is less than are equal to

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x is less than or equal to to pi As

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fate would have it speed of the slowest dog in

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town is in line to try to solve her question

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he grabs the marker and begin solving the equation by

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factoring the expression If we factor the expression tangents squared

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of x minus three like the difference of two squares

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will have the expression the quantity tangent of x minus

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square root of three times the quantity tangent of ax

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plus square root of three In a bold move he

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is now setting each of the quantities equal to zero

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He knows that if their product together is zero then

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one or both of them must be equal to zero

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Solving each of the equations with a speed we frankly

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

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equations using a technique he must have studied with his

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trigonometry teacher He is taking the inverse tangent of both

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of the equations to solve for x reaching far back

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into the recesses of his canine brain He recalls that

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the inverse tangent of route three is pi over three

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And the inverse tangent of negative Ruth 3 is 2

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

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within an interval of pie because both pie over three

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and two pi over three are less than pie That

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makes sense because the tangent function has a period of

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pi which means it goes through one full cycle for

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every pie radiance Since speedy is looking for all answered

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between zero and two pie he has to consider the

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

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find those values he needs tto add pie each of

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the answers he already has So who had pi tau

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pi over three We must first make sure both numbers

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have the same denominator We can multiply three over three

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And a pie to make it have the common denominator

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of three When adding fractions we add across the top

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and keep the denominator the same so three pi over

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three plus pie over three equals four pi over three

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brad pie to two pi over three We again have

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to make sure both numbers are under the same denominator

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we can again multiply three over three two pie to

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get three pi over three plus two by over three

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adding across the top Numbers we get 3 pie plus

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two pi equals five pie over three Those final answers

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are x equals pi over three four pi over three

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two pi over three and five pie over three Unbelievable

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speedy has solved the trig equation Unfortunately the dunk tank

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malfunctions and calico gets drenched anyway Sh

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