b. Whatis the soundlevel (in ) of a soundwhoseintensityis?
Referringto problem#6, a singlemosquito metersawayfrom a personmakesa soundthat is barely
heardby the person(threshold ). Whatwill be the soundlevel of mosquitoesat the samedis-
tance?
Referringbackto problem#6, a noisymachineat a factoryproducesa soundlevel of If an iden-
tical machineis placedbesideit, whatis the combinedsoundlevel of the two machines?
Answers
a. millionb. 2077
Hint: use
seconds,about minutes
grams
a. b.
Derivativesand IntegralsInvolvingInverseTrigonometricFunctions
LearningObjectives
A studentwill be able to:
- Learnthe basicpropertiesinversetrigonometricfunctions.
- Learnhow to use the derivativeformulato use themto find derivativesof inversetrigonometricfunctions.
- Learnto solvecertainintegralsinvolvinginversetrigonometricfunctions.
A QuickAlgebraicReviewof InverseTrigonometricFunctions
You alreadyknowwhata trigonometricfunctionis, but whatis an inversetrigonometricfunction?If we ask
whatis equalto, the answeris That is simpleenough.But whatif we ask whatanglehas
a sine of (1/2)? That is an inverse trigonometric function. So we say but
The “ ” is the notationfor the inverseof the sine function.For everyone of
the six trigonometricfunctionsthereis an associatedinversefunction.Theyare denotedby