1. 5.8 Inverse Trig Functions

2. Definition of Inverse Trig Functions

3. Graphs of inverse functions
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4. Ex. 1 Evaluating Inverse Trig Functions
a)arcsin(-1/2)
b)arcsin(0.3)

5. 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

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

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

8. Ex 3 cont…

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

11. Derivatives of Inverse Trig Functions

12. Ex. 5 Find the derivative a) b)

13. Ex 5. cont… c) d)