TRIGONOMETRY

TRIGONOMETRYWith Tony the Triangle!!!

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SineTangent

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Cosine

SOH-CAH-TOA

In Trigonometry the three basic functions that

we will be learning about can be remembered

by the pneumonic below:

SOH-CAH-TOAMove

on!

Directions

• Read through the descriptions and applications of each of the trig functions

• Complete the quiz at the end of each section• Have your instructor come around when you

have completed the quiz to gain participation points

• Complete the final evaluation at the end of the presentation!

• Click the pink triangles to continue Move on!

I just need to review one function

Sine Cosine Tangent

I want to go through the whole presentation

Let’s Go!

Other OptionsLife

ApplicationsI’m Ready! Quiz Me!

The Sine Function

Sine comes from the SOH part of

soh-cah-toa

Sine equals Opposite over Hypotenuse

SOH

Opp

osite

Hypotenuse

Sin( )= HypotenuseOpposite

Uses for the Sine Function

When given a right angle triangle with an angle theta, and the length of the opposite side, the sine function can be used to compute the length of the hypotenuse of the given triangle.

=30 degrees

Opp. Side = 1

Opp

osite

Sin(30)= 1/hypotenuse(Hypotenuse)(Sin(30))=1Hypotenuse = 2

More uses for Sine… When given a right angle triangle

with the length of the hypotenuse and the length of the opposite side, the sine function can be used to compute the measure of the angle theta.

Hypotenuse

Opp

ositeOpp. Side = 1

Hypotenuse= sqrt(2)

Sin( )= 1/sqrt(2) =45 degrees or pi/4 radians

And even one more use!

When given a right angle triangle with an angle theta, and the length of the hypotenuse, the sine function can be used to compute the length of the opposite side of the given triangle.

Hypotenuse

Hypotenuse= 2=60 degrees

Sin(60)= opposite side/22(Sin(30))=Opposite sideOpposite side = 1

Sine Quiz Time!!!

What is the value of the opposite side?

=45 degrees

Hypotenuse= sqrt(2)

Hypotenuse

0

1

2

Tony the Triangle Says…

Sorry! Try again!

Back to Sine


You got it!

Back to the Menu

On to Cosine

The Cosine Function

Cosine comes from the CAH part

of soh-cah-toa

Cosine equals Adjacent over Hypotenuse

CAHAdjacent

Hypotenuse

Cos( )= HypotenuseAdjacent

Uses for the Cosine Function

When given a right angle triangle with an angle theta, and the length of the adjacent side, the cosine function can be used to compute the length of the hypotenuse of the given triangle.

=30 degrees

Adj. Side = sqrt(3)

AdjacentCos(30)= sqrt(3)/Hypotenuse(Hypotenuse)(Cos(30))=sqrt(3)Hypotenuse = 2

More uses for Cosine… When given a right angle triangle

with the length of the hypotenuse and the length of the adjacent side, the cosine function can be used to compute the measure of the angle theta.

HypotenuseAdj. Side = 1Hypotenuse= sqrt(2)

Cos( )= 1/sqrt(2) =45 degrees or pi/4 radians

Adjacent

And even one more use!

When given a right angle triangle with an angle theta, and the length of the hypotenuse, the cosine function can be used to compute the length of the adjacent side of the given triangle.

Hypotenuse

Hypotenuse= 2=60 degrees

Sin(60)= Adjacent side/22(Sin(30))=Adjacent SideAdjacent side = 1

Cosine Quiz Time!!!

Which variable can be found using cosine

Hypotenusey

none

x

Theta=45 deg.Hypotenuse=sqrt(2)

y

x


Get it next time!

Back to Cosine


Way to go!

Back to the Menu

On to Tangent

The Tangent Function

Tangent comes from the TOA part

of soh-cah-toa

Tangent equals Opposite over Adjacent

TOAAdjacent

Tan( )= AdjacentOpposite

Opp

osite

Uses for the Tangent Function

When given a right angle triangle with an angle theta, and the length of the adjacent side, the tangent function can be used to compute the length of the opposite side of the given triangle.

=30 degrees

Adj. Side = sqrt(3)

AdjacentTan(30)= (1/sqrt(3))/Opposite(Opposite)(Tan(30))=(1/sqrt(3))Opposite=1

More uses for Tangent… When given a right angle triangle

with the length of the opposite side and the length of the adjacent side, the tangent function can be used to compute the measure of the angle theta.

Adj. Side = 1Opposite=1

Tan( )= 1/1 =45 degrees or pi/4 radians

Adjacent

And even one more use! When given a right angle triangle

with an angle theta, and the length of the opposite side, the cosine function can be used to compute the length of the adjacent side of the given triangle.

Opposite= 2=45 degrees

Tan(45)= 2/(Adjacent Side)2=(Tan(45))(Adjacent Side)Adjacent side = 2

Tangent Quiz Time!!!

What Ratio describes the tangent function?

2/1

8/6

3/4

6

8


You’re so close!

Back to Tangent


That was Fantastic!

Back to the Menu

On to Applications

You’re probably wondering…

Why should I care?

When will we ever us this?

How does this affect me?

Find Out!

Applications

• In this picture we can find the height of the tree using our distance from the tree and the angle of inclination.

How tall is the tree?

We are 20 feet from the tree and our angle of inclination is 45 degrees with our head at ground level.

804020


Check those applications

again!

Back to Applications


Keep on truckin’!

Back to the Menu

To the final Quiz!


You can do it!!!!

Get ready for 3 questions in a row

Question #1

What is the value of r?

=pi/4

r

0

1

Sqrt(2)

1


Back to square 1!

Back to the 1st question


You got this!

Next Question

Question #2

What kind of triangle do these trigonometric functions apply to?

Equilateral

Right

neither


Almost had it. Keep trying!

Back to the 1st question


Wow! That’s

impressive!

Next Question

Question #3

Which function(s) can be used to find r?

=30

rSine Cosine

Tangent

1

Sqrt(3)

Sine and

Cosine


So close!

Try quiz again


Congrats!!!

ReviewTony the Triangle would like to congratulate you

on mastering these functions!

TRIGONOMETRY

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