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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!
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.
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.
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
The Cosine Function
Cosine comes from the CAH part
of soh-cah-toa
Cosine equals Adjacent over Hypotenuse
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.
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
The Tangent Function
Tangent comes from the TOA part
of soh-cah-toa
Tangent equals Opposite over Adjacent
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.
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.
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
Question #2
What kind of triangle do these trigonometric functions apply to?
Equilateral
Right
neither
Question #3
Which function(s) can be used to find r?
=30
rSine Cosine
Tangent
1
Sqrt(3)
Sine and
Cosine
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