Inverse Trig Functions

Presentation

•

Mathematics

•

10th Grade

•

Easy

•

CCSS

HSF.TF.A.2, 8.G.B.8

Standards-aligned

Anna Cockrum

Used 26+ times

FREE Resource

9 Slides • 2 Questions

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^-1we 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

Type response here

Find all missing measurements

$m\angle D\ =\ 55\degree$
$m\angle E\ =\ 35\degree$
$EF\ =\ 5.7\ units$

Inverse Trig Functions

Monday March 1, 2021

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