1 / 14

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.

amanda
Download Presentation

Ms. Battaglia AP Calculus

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related