# Solving Trigonometric Equations

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 Model periodic phenomena with trigonometric functions Prove and apply trigonometric identities |

Geometry | Angles Define trigonometric ratios and solve problems involving right triangles Similarity, right triangles, trigonometry, and dimensions |

Language | English Language |

Precalculus | Trigonometric Functions |

Right Triangles and Trigonometry | Basic Trig Ratios |

Similarity, Right Triangles, and Trigonometry | Define trigonometric ratios and solve right triangle problems |

Systems of Equations | Linear and Nonlinear Equations |

Trigonometric Functions | Basic Trig Functions Inverses |

### Transcript

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

metric equations tangent squared of x minus three equals zero

For the interval zero is less than are equal to

x is less than or equal to to pi As

fate would have it speed of the slowest dog in

town is in line to try to solve her question

he grabs the marker and begin solving the equation by

factoring the expression If we factor the expression tangents squared

of x minus three like the difference of two squares

will have the expression the quantity tangent of x minus

square root of three times the quantity tangent of ax

plus square root of three In a bold move he

is now setting each of the quantities equal to zero

He knows that if their product together is zero then

one or both of them must be equal to zero

Solving each of the equations with a speed we frankly

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

equations using a technique he must have studied with his

trigonometry teacher He is taking the inverse tangent of both

of the equations to solve for x reaching far back

into the recesses of his canine brain He recalls that

the inverse tangent of route three is pi over three

And the inverse tangent of negative Ruth 3 is 2

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

within an interval of pie because both pie over three

and two pi over three are less than pie That

makes sense because the tangent function has a period of

pi which means it goes through one full cycle for

every pie radiance Since speedy is looking for all answered

between zero and two pie he has to consider the

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

find those values he needs tto add pie each of

the answers he already has So who had pi tau

pi over three We must first make sure both numbers

have the same denominator We can multiply three over three

And a pie to make it have the common denominator

of three When adding fractions we add across the top

and keep the denominator the same so three pi over

three plus pie over three equals four pi over three

brad pie to two pi over three We again have

to make sure both numbers are under the same denominator

we can again multiply three over three two pie to

get three pi over three plus two by over three

adding across the top Numbers we get 3 pie plus

two pi equals five pie over three Those final answers

are x equals pi over three four pi over three

two pi over three and five pie over three Unbelievable

speedy has solved the trig equation Unfortunately the dunk tank

malfunctions and calico gets drenched anyway Sh