Alternatively, you may see the followingnotationsfor the aboveinverses,respectively,
Sinceall trigonometricfunctionsare periodicfunctions,they do not passthe horizontalline test. Therefore
they are not one-to-onefunctions.The tablebelowprovidesa brief summaryof their definitionsand basic
properties.We will restrictour studyto the first four functions;the remainingtwo, and are of
lesserimportance(in mostapplications)and will be left for the exercises.
InverseFunction Domain Range BasicPropertiesallThe rangeis basedon limitingthe domainof the originalfunctionso that it is a one-to-onefunction.
Example1:
Whatis the exactvalueof?
Solution:
This is equivalentto. Thus. You can easilyconfirmthis resultby using
your scientificcalculator.
Example2:
Mostcalculatorsdo not providea way to calculatethe inverseof the secantfunction, A practical
trick howeveris to use the identity
(Recallthat )
For practice,use your calculatorto find
Solution:
Since