Ms battaglia ap calculus
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5-6 Inverse Trig Functions: Differentiation (Day 2) Objective: Develop properties of the 6 inverse trig functions and differentiate an inverse trig function. Ms. Battaglia AP Calculus. Definitions of Inverse Trig Functions. Graphs of Inverse Trig Functions. y = arcsinx y = arccosx.

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Ms. Battaglia AP Calculus

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Ms battaglia ap calculus

5-6 Inverse Trig Functions: Differentiation (Day 2)Objective: Develop properties of the 6 inverse trig functions and differentiate an inverse trig function.

Ms. Battaglia

AP Calculus


Definitions of inverse trig functions

Definitions of Inverse Trig Functions


Graphs of inverse trig functions

Graphs of Inverse Trig Functions

y = arcsinxy = arccosx


Graphs of inverse trig functions1

Graphs of Inverse Trig Functions

y = arctanxy = arccscx


Graphs of inverse trig functions2

Graphs of Inverse Trig Functions

y = arcsecxy = arccotx


Evaluating inverse trig functions

Evaluating Inverse Trig Functions

a.b.

c.d.


Properties of inverse trig functions

Properties of Inverse Trig Functions

If -1 < x < 1 and –π/2 < y <π/2 then

sin(arcsinx) = x and arcsin(siny) = y

If –π/2 < y < π/2, then

tan(arctanx) = x and arctan(tany) = y

If |x| > 1 and 0 < y < π/2 or π/2 < y < π, then

Sec(arcsecx) = x and arcsec(secy) = y.

Similar properties hold for other inverse trig functions.


Solving an equation

Solving an Equation

Arctan(3x – π) = 1/2


Using right triangles

Using Right Triangles

  • Evaluate sin(arctan(3/4))

  • Evaluate sec(arsin(4/5))


Derivatives of inverse trig functions

Derivatives of Inverse Trig Functions

Let u be a differentiable function of x.


Differentiating inverse trig functions

Differentiating Inverse Trig Functions

a.

b.

c.

d.


Analyzing an inverse trig graph

Analyzing an Inverse Trig Graph

Analyze the graph of f(x) = arctanx + π/2


See page 378 for a review of basic differentiation rules for elementary functions

See Page 378 for a Review of Basic Differentiation Rules for Elementary Functions.


Classwork homework

Classwork/Homework

  • AB: Page 380 #63, 64, 65, 77, 91-93


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