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Ms. Battaglia AP CalculusPowerPoint Presentation

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

Graphs of Inverse Trig Functions

y = arcsinx y = arccosx

Graphs of Inverse Trig Functions

y = arctanx y = arccscx

Graphs of Inverse Trig Functions

y = arcsecx y = arccotx

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.

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 Elementary Functions.

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

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