Lesson 17: Inverse Trigonometric Functions

Section 3.5Inverse TrigonometricFunctionsV63.0121, Calculus IMarch 11–12, 2009AnnouncementsGet half of your unearned ALEKS points back by March 22What functions are invertible?In order for f−1 to be a function, there must be only one a in Dcorresponding to each b in E.Such a function is called one-to-oneThe graph of such a function passes the horizontal line test:any horizontal line intersects the graph in exactly one point if atall.If f is continuous, then f−1 is continuous.OutlineInverse Trigonometric FunctionsDerivatives of Inverse Trigonometric FunctionsArcsineArccosineArctangentArcsecanty = xarcsinThe domain of arcsin is [−1, 1][]πThe range of arcsin is − π ,2 2arcsinArcsin is the inverse of the sine function after restriction to[−π/2, π/2].yxsin−π−π22y = xarcsinThe domain of arcsin is [−1, 1][]πThe range of arcsin is − π ,2 2arcsinArcsin is the inverse of the sine function after restriction to[−π/2, π/2].yxsin−π−π22arcsinThe domain of arcsin is [−1, 1][]πThe range of arcsin is − π ,2 2arcsinArcsin is the inverse of the sine function after restriction to[−π/2, π/2].yy = xxsin−π−π22y = xarcsinArcsin is the inverse of the sine function after restriction to[−π/2, π/2].yarcsinxsin−π−π22The domain of arcsin is [−1, 1][]πThe range of arcsin is − π ,2 2arccosy = xThe domain of arccos is [−1, 1]The range of arccos is [0, π]arccosArccos is the inverse of the cosine function after restriction to [0, π]ycosx0πarccosy = xThe domain of arccos is [−1, 1]The range of arccos is [0, π]arccosArccos is the inverse of the cosine function after restriction to [0, π]ycosx0πarccosThe domain of arccos is [−1, 1]The range of arccos is [0, π]arccosArccos is the inverse of the cosine function after restriction to [0, π]yy = xcosx0πDocument Outline

• Announcements
• Inverse Trigonometric Functions
• Derivatives of Inverse Trigonometric Functions
  • Arcsine
  • Arccosine
  • Arctangent
  • Arcsecant