trigonometry with tony the triangle!!! let’s have some fun! click me!
TRANSCRIPT
TRIGONOMETRYWith Tony the Triangle!!!
Let’s have some fun!
Click me!
SineTangent
Let’s Get Started!
Where to start…
Click here to begin
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
Tony the Triangle Says…
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
Tony the Triangle Says…
Get it next time!
Back to Cosine
Tony the Triangle Says…
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
Tony the Triangle Says…
You’re so close!
Back to Tangent
Tony the Triangle Says…
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
Tony the Triangle Says…
Check those applications
again!
Back to Applications
Tony the Triangle Says…
Keep on truckin’!
Back to the Menu
To the final Quiz!
Tony the Triangle Says…
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
Tony the Triangle Says…
Back to square 1!
Back to the 1st question
Tony the Triangle Says…
You got this!
Next Question
Question #2
What kind of triangle do these trigonometric functions apply to?
Equilateral
Right
neither
Tony the Triangle Says…
Almost had it. Keep trying!
Back to the 1st question
Tony the Triangle Says…
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
Tony the Triangle Says…
So close!
Try quiz again
Tony the Triangle Says…
Congrats!!!
ReviewTony the Triangle would like to congratulate you
on mastering these functions!