1 / 9

1.7

1.7 . Inverse Trig Functions Sin,cos,tan. The goal is to find, define and graph the inverse trig functions. An inverse function undoes another function. For example y = x 2 and y = √x Are inverses because they “undo” each other.

lavada
Download Presentation

1.7

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. 1.7 Inverse Trig Functions Sin,cos,tan

  2. The goal is to find, define and graph the inverse trig functions. An inverse function undoes another function. For example y = x2 and y = √x Are inverses because they “undo” each other. For our trig inverse functions were are going to put in values and get out angles.

  3. We choose the portion of y= cos(x) from x = 0 to x = π. We now reflect every point on this portion of the cos x curve through the line y = x.

  4. Inverse Cos or arccos Dom: [-1,1] Range: [0, π]

  5. we reflect the indicated portion of y = sin x through the line y = x, we obtain the graph of y = arcsin x:

  6. Inverse Sin or arcsin We are now putting In values and Getting out Angles. We always Restrict the inverse Graphs. Dom [-1,1] Range [-π/2, π/2]

  7. Reflecting this portion of the graph in the line y = x, we obtain the graph of y = arctan x The domain of arctan x is All values of x The range for arctan x is -π/2 ≤ arctan x ≤ π/2

  8. arctan is the same as tan inverse or tan-1. y = tan-1x = arctan We put in values and get out angles. Ex. sin-1(√2/2) = arcsin (√2/2) = what angle has a sin value of √2/2 and is between -π/2, π/2 = π/4 Functions and their inverses undo each other arcsin(sin(x)) = x

  9. HW pg 197 1-15 odd Draw arccos, arcsin, and arctan

More Related