 # Inverses  How do we know if something has an inverse? ○ Vertical line tests tell us if something is a function ○ Horizontal line tests will tell us if.

## Presentation on theme: "Inverses  How do we know if something has an inverse? ○ Vertical line tests tell us if something is a function ○ Horizontal line tests will tell us if."— Presentation transcript:

Inverses  How do we know if something has an inverse? ○ Vertical line tests tell us if something is a function ○ Horizontal line tests will tell us if there is an inverse.  Do any of the 6 trig functions have inverses? ○ What if we restricted what we were looking at…

Inverse Sine Function “Arcsine Function”

Evaluate without a Calculator You can only have answers between [-π/2, π/2]  sin -1 ( 1 / 2 )  sin -1 (- √3 / 2 )

Evaluate without a Calculator You can only have answers between [-π/2, π/2]  sin -1 ( π / 2 )  sin -1 (sin( π / 9 ))  sin -1 (sin( 5π / 6 ))

Evaluate with a Calculator Use the “2 nd ” button and the “sin” button.  sin -1 (-.081)  sin -1 (sin(3.49π))  sin -1 (3)

Inverse Cosine Function

Evaluate without a Calculator  cos -1 (- √2 / 2 )  cos -1 (cos(-1.1))

Inverse Tangent Function

Evaluate without a Calculator  tan -1 (√3)  tan -1 (-1)

Evaluate with a Calculator  sin -1 (0.362) in degrees  tan -1 (-12.5) in degrees  tan -1 (2.37) in radians  sin -1 (-0.46) in radians

Evaluate without a Calculator  cos(sin -1 ( 1 / 2 ))  sin -1 (cos( π / 4 ))  arcsin(cos( π / 3 ))  cos(tan -1 (√3))

Download ppt "Inverses  How do we know if something has an inverse? ○ Vertical line tests tell us if something is a function ○ Horizontal line tests will tell us if."

Similar presentations