Inverse Trig Functions Modified from the lesson at: Functions....%20Cached%20Similar.

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Presentation transcript:

Inverse Trig Functions Modified from the lesson at: Functions....%20Cached%20Similar

* Start with Sine Function  Given y = sin (x)

* Start with Sine Function  Given y = sin (x)  Table of values xy = sin(x)

* Start with Sine Function  Given y = sin (x)  Table of values  Graph xy = sin(x)

* Start with Sine Function  Given y = sin (x)  Table of values  Graph xy = sin(x) What if we reversed the ordered pairs … y for x ?

* Reversed Ordered Pairs xy

* Reversed Ordered Pairs  Problem This is not a function Fails the vertical line test There are multiple (x,y)'s where x =.5 xy

* Reversed Ordered Pairs  Problem This is not a function Fails the vertical line test There are multiple (x,y)'s where x =.5  Solution Limit the range xy

* The Inverse Trig Function  We say  Similarly for inverse cosine  The range of cos -1 x is limited differently

* Evaluating Inverse Functions  Consider cos -1 (-0.5) We are asking what angle has a cosine value of -0.5

* Evaluating Inverse Functions  Consider cos -1 (-0.5) We are asking what angle has a cosine value of -0.5  Cosine negative in quadrants 2 and 3 But for cos -1 (x) we look only in 1 & 2

* Evaluating Inverse Functions  Consider cos -1 (-0.5) We are asking what angle has a cosine value of -0.5  Cosine negative in quadrants 2 and 3 But for cos -1 (x) we look only in 1 & 2 2

* Evaluating Inverse Functions  Consider cos -1 (-0.5) We are asking what angle has a cosine value of -0.5  Cosine negative in quadrants 2 and 3 But for cos -1 (x) we look only in 1 & 2 2 Calculator also capable of evaluating inverse trig functions

* Evaluating Inverse Functions  Consider cos -1 (-0.5) We are asking what angle has a cosine value of -0.5  Cosine negative in quadrants 2 and 3 But for cos -1 (x) we look only in 1 & 2 2 Calculator also capable of evaluating inverse trig functions

* Try It Out  Consider these

* Try It Out  Consider these

* Try It Out  Consider these

_Screen/Function_Keys/trig_keys/trig_keys.html Calculator Notes Cosecant, Secant, and Cotangent are not built in to the TI-83 or the TI-84 so you will have to use the reciprocal key or put the expression in rational form to evaluate. You have to be careful with coefficients. The coefficients should not be placed in the denominator.

* Try It Out  Consider these

Try It Out  Consider these

Composition of Trig Functions and Inverses  Try these …

Composition of Trig Functions and Inverses  Try these …

Composition of Trig Functions and Inverses  Try these …

Composition of Trig Functions and Inverses  Try these …