Inverse Trigonometric Functions

Inverse Trig Functions

Monday March 1, 2021

Multiple Choice

Trig Functions tell us what?

• sides

• angles

• Relationship between the ratio of side lengths at a given angle

• nothing

Trig so far...

Up to this point we have only been able to solve for side lengths using trig.

 $\theta$  is a place holder for an angle measure (it's a number)

 $\sin\left(\theta\right)=\frac{opposite}{hypotenuse}$   $\cos\left(\theta\right)=\frac{adjacent}{hypotenuse}$  

 $\tan\left(\theta\right)=\frac{opposite}{adjacent}$  

What if we want to solve for an angle?

Then we need to use inverse functions

Inverse Trig Functions Notations

• There are two types of notation for inverse functions:

• arcsin, arccos, arctan

• sin^-1, cos^-1, tan^-1

• REGARDLESS OF NOTATION WE ALWAYS SAY "inverse" never "arc" or "to the -1"

• arcsin = sin^-1 we say "inverse sine" or "sine inverse"

• arccos = cos^-1 we say "inverse cossine" or "cosine inverse"

• arctan = tan^-1 we say "inverse tangent" or "tangent inverse"

use the 2nd button to access the functions above the buttons (they're printed in a light blue or white)

When you tap 2nd it turns gray, and you see the inverse functions for sine, cosine, and tangent

Find all missing measurements

•  $m\angle B\ :\ \arccos\left(\frac{9}{10}\right)\$   $=\ \cos^{-1}\left(\frac{9}{10}\right)\ =\ 25.8\degree\ \rightarrow26\degree$  

• You can use Pythagorean Theorem to solve for missing side

• Now that you know an acute angle, you can just subtract from 90

Open Ended

Find all missing measurements

Find all missing measurements

•  $m\angle D\ =\ 55\degree$  

•  $m\angle E\ =\ 35\degree$  

•  $EF\ =\ 5.7\ units$