5.8 Inverse Trig Functions

Definition of Inverse Trig Functions

Graphs of inverse functions Page 381

Ex. 1 Evaluating Inverse Trig Functions a)arcsin(-1/2) b)arcsin(0.3)

Properties of Inverse Functions If -1≤x≤1 and –π/2≤y≤π/2, then: sin(arcsin x)=x and arcsin(sin y)=y If –π/2≤y≤π/2, then tan(arctan x)=x and arctan(tan y)=y If |x|≥1 and 0≤y≤π/2 or π/2≤y≤π, then sec(arcsec x)=x and sec(arcsec y)=y Similar properties hold true for the other trig functions

Solving an Equation arctan(2x – 3) = π/4

Ex. 3 Use Right Triangles to Solve Find cos(arcsin x), where 0≤y≤π/2

Ex 3 cont…

Ex 4 Write the expression in algebraic form cos(arcsin 2x)

Derivatives of Inverse Trig Functions

Ex. 5 Find the derivative a) b)

Ex 5. cont… c) d)