7.6 Inverse Trig Functions

7.6: Inverse Trigonometric Functions

• Inverse Functions

                                      Where u is the value of a trig function of angle v  

                

              Properties of Inverse Functions

It is important to note that depending on your book,:

• Inverse Sine

or

IMPORTANT! :

                Properties of Inverse Sine

• Inverse Cosine

or

IMPORTANT! :

                   Properties of Inverse Cosine



• Inverse Tangent

or

                Properties of Inverse Tangent

                         y= tan x                                                          y= arctan x

S.O.S!

   When given an angle of inverse sine or inverse tangent, the angle value is restircted to the first and fourth quadrents.  This will help a lot when solving equations.  When given an inverse cosine, the angle is within the first and second quadrents.  Here is an image Mr. Bruns gave us to Help:

 Hope this helps! 6 days till the return of Wilhelm! AHH!
Blessing, EmJ

6.5 Trigonometric Graphs

TRIGONOMETRIC GRAPHS

Graphing      :

Graphing      :

Graphing      :

• 'a' leads to vertical stretching. Vertical stretching will cause a change in amplitude.
• 'b' leads to horizontal compressing. Horizontal compressing will change the period.
• 'c' leads to shifting left or right. This left or right shifting is called a phase shift.
• 'd' leads to shifting up or down. This up or down shift is called a midline shift because it will affect the midline.

VERTICAL STRETCHING

 compared to 

AMPLITUDE/PERIOD

HORIZONTAL COMPRESSING

 compared to

L/R SHIFT (PHASE SHIFT)

 compared to              compared to 

The graph on the left is showing a left phase shift. The graph on the right shows a right phase shift.

U/D SHIFT (MIDLINE SHIFT)

This graph shows an upward midline shift.

This graph shows a downward midline shift.

MIDLINE

This graph shows 

 & in the thinner and wavy lining and their midline's in a thick line through the middle of each.

And that's about it, other than The Nonagon Song, of course.

Alex Hackert