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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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 = arcsinxy = arccosx


Graphs of Inverse Trig Functions

y = arctanxy = arccscx


Graphs of Inverse Trig Functions

y = arcsecxy = arccotx


Evaluating Inverse Trig Functions

a.b.

c.d.


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

Arctan(3x – π) = 1/2


Using Right Triangles

  • Evaluate sin(arctan(3/4))

  • Evaluate sec(arsin(4/5))


Derivatives of Inverse Trig Functions

Let u be a differentiable function of x.


Differentiating Inverse Trig Functions

a.

b.

c.

d.


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.


Classwork/Homework

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


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