CK12 - Trigonometry

For example,a rationalfunctionis usedto modelinversevariationbetweentwo variables.Inversevariation

meansthat the productof two variablesis constant:xy=k. If we solvethis equationfory,we have
, a rationalfunction.The followingexampleshowsinversevariationin a real situation:

Example4:Somedaysyou driveto work,and otherdaysyou ride your bike.Yesterdayyou droveat an
averagerate of 40 milesper hour, and it took 15 minutes.Todayyou rode your bike a rate of 20 milesper
hour, and it took half an hour.

Write an equationthat showsthe relationshipbetweenyour speedand the time it takesto get to work.

Solution: , wherexis your speedin milesper hour andyis the time it takesto get to workin hours.

First,note that the distancebetweenhomeand workis 10 miles:

We knowthat in general:

Thereforeif you driveor ride at a rate ofxmilesper hour, it will take youyhoursto get to work:.

In general,functionscan be usedto modelreal phenomenain manycontexts,includingdifferentareasof
science,business,economics,and more.The type of functionthat can be usedto modela specificsituation
dependson the key aspectsof a functionthat will matchkey aspectsof the situation.One aspectof many
situationsis not seenin the functiontypeswe haveseenso far, but will be seenin the trigonometricfunctions
you will learnaboutin this chapter. Considerfor example,the tablebelow, whichshowsthe averagemonthly
high and low temperaturesin the city of Boston,MA, from 1971to 2000.(Source:rssweather.com)

Month Low High

Jan 22.1oF 36.5oF

Feb 24.2oF 38.7oF

Mar 31.5oF 46.3oF

56.

o

40.5 F

o

Apr F