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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. Graphs of Inverse Trig Functions. y = arcsinx y = arccosx.

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Ms. Battaglia AP Calculus

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  1. 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

  2. Definitions of Inverse Trig Functions

  3. Graphs of Inverse Trig Functions y = arcsinx y = arccosx

  4. Graphs of Inverse Trig Functions y = arctanx y = arccscx

  5. Graphs of Inverse Trig Functions y = arcsecx y = arccotx

  6. Evaluating Inverse Trig Functions a. b. c. d.

  7. 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.

  8. Solving an Equation Arctan(3x – π) = 1/2

  9. Using Right Triangles • Evaluate sin(arctan(3/4)) • Evaluate sec(arsin(4/5))

  10. Derivatives of Inverse Trig Functions Let u be a differentiable function of x.

  11. Differentiating Inverse Trig Functions a. b. c. d.

  12. Analyzing an Inverse Trig Graph Analyze the graph of f(x) = arctanx + π/2

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

  14. Classwork/Homework • AB: Page 380 #63, 64, 65, 77, 91-93

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