1 / 13

5.8 Inverse Trig Functions

5.8 Inverse Trig Functions. Definition of Inverse Trig Functions. Graphs of inverse functions. Page 381. Ex. 1 Evaluating Inverse Trig Functions. a) arcsin (-1/2) b) arcsin (0.3). Properties of Inverse Functions. If -1≤x≤1 and – π /2≤y≤ π /2, then: sin( arcsin x)=x and arcsin (sin y)=y

winona
Download Presentation

5.8 Inverse Trig Functions

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. 5.8 Inverse Trig Functions

  2. Definition of Inverse Trig Functions

  3. Graphs of inverse functions • Page 381

  4. Ex. 1 Evaluating Inverse Trig Functions • a)arcsin(-1/2) • b)arcsin(0.3)

  5. Properties of Inverse Functions • If -1≤x≤1 and –π/2≤y≤π/2, then: • sin(arcsin x)=x and arcsin(sin y)=y • If –π/2≤y≤π/2, then • tan(arctan x)=x and arctan(tan y)=y • If |x|≥1 and 0≤y≤π/2 or π/2≤y≤π, then • sec(arcsec x)=x and sec(arcsec y)=y • Similar properties hold true for the other trig functions

  6. Solving an Equation • arctan(2x – 3) = π/4

  7. Ex. 3 Use Right Triangles to Solve • Find cos(arcsin x), where 0≤y≤π/2

  8. Ex 3 cont…

  9. Ex 4 Write the expression in algebraic form • cos(arcsin 2x)

  10. Derivatives of Inverse Trig Functions

  11. Ex. 5 Find the derivative • a) • b)

  12. Ex 5. cont… • c) • d)

More Related