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Army Daniel
SOH-CAH-TOA EAST OF SOH-CAH-TOA EAST OF JAVAJAVA
[Exploring Trigonometric Functions]
Army Daniel
SOH-CAH-TOA SOH-CAH-TOA means many thingsmeans many things
“Hello” “Goodbye” “I love you” “Your slip is showing”“It’s Your turn to take out the trash!!!”
Army Daniel
SOHCAHTOA Also Means: SOHCAHTOA Also Means: “Let’s do Trig!!“Let’s do Trig!!
[SOH] Sine – Opposite – Hypotenuse
[CAH] Cosine – Adjacent – Hypotenuse
[TOA] Tangent – Opposite - Adjacent
Army Daniel
First: A quick Geometry First: A quick Geometry ReviewReview
PARTS
OF A
RIGHT
TRIANGLE
OPPOSITE
ADJACENT
HYPOTENUSE
Army Daniel
So, Sohcahtoa!So, Sohcahtoa!
[…trans. “Let’s do Trig.!”][…trans. “Let’s do Trig.!”]
Army Daniel
We’ll break it into syllables.We’ll break it into syllables.
Army Daniel
SOHSOH-CAH-TOA-CAH-TOA
Army Daniel
SOH: SINE-SOH: SINE-OPPOPP-HYP-HYP
sin = opposite side
hypotenuse
OPPOSITE
ADJACENT
HYPOTENUSE
Army Daniel
SOH-SOH-CAHCAH-TOA-TOA
Army Daniel
CAH: COSINE-CAH: COSINE-ADJADJ-HYP-HYP
cos = adjacent side
hypotenuse
OPPOSITE
ADJACENT
HYPOTENUSE
Army Daniel
SOH-CAH-SOH-CAH-TOATOA
Army Daniel
TOA: TAN-TOA: TAN-OPPOPP--ADJADJ
tan = opposite side
adjacent
OPPOSITE
ADJACENT
HYPOTENUSE
Army Daniel
A QUICK REVIEWA QUICK REVIEW
SOH - sin = Opposite side
Hypotenuse
CAH - cos = Adjacent side
Hypotenuse
TOA - tan = Opposite side
Adjacent side
Army Daniel
APPLICATIONS:APPLICATIONS:
Let’s solve a problem.
Sohcahtoa!
Army Daniel
Check for Understanding.Check for Understanding.
Find
sin =
cos =
tan =
3
4
5
Army Daniel
Check : Don’t Forget!Check : Don’t Forget!
Find
sin = OPP
HYP
cos = ADJ
HYP
tan = OPP
ADJ
3
ADJ
4 OPP
5 HYP
Army Daniel
Check : ANSWERSCheck : ANSWERS
Find
sin = OPP = 4
HYP 5
cos = ADJ = 3
HYP 5
tan = OPP = 4
ADJ 3
3
ADJ
4 OPP
5 HYP
Army Daniel
APPLICATIONS:APPLICATIONS:
Let’s try a different problem.
Sohcahtoa!
Army Daniel
Check for Understanding.Check for Understanding.
Find x
given: cos 60° = 0.5
60°
x
1
Army Daniel
Check for Understanding.Check for Understanding.
Find x
given: cos 60° = 0.5
And don’t forget
SOH-CAH-TOA60°
x
1
Army Daniel
Check : ANSWERCheck : ANSWER
X = 2
How?
60°
x
1
Army Daniel
Check : ANSWERCheck : ANSWER
X = 2
How? Use
SOH – CAH - TOA
cos 60° = .5 = ADJ = 1
HYP x
.5x = 1
x = 2
60°
x
1
Army Daniel
APPLICATIONS:APPLICATIONS:
Let’s try a WORD problem!
Sohcahtoa!
Army Daniel
Find the Height of Mt. Find the Height of Mt. SohcahtoaSohcahtoa
The volcano is rumbling. The Sohcahtoans need to sacrifice a virgin. They know the base of the mountain is 6 miles high. The angle formed from the base to the top is 60°.
How tall is the mountain?
[Use your calculator!!!]
Army Daniel
Find the Height of Mt. Find the Height of Mt. SohcahtoaSohcahtoa
What do we know?
= 60°
Base = 6 miles = 3 miles
2
6 miles
Height
Army Daniel
What else do know?What else do know?
SOH - sin = Opposite side
Hypotenuse
CAH - cos = Adjacent side
Hypotenuse
TOA - tan = Opposite side
Adjacent side
Which one should we use?
6 miles
Height
Army Daniel
Which one?Which one?
SOH - sin = Opposite side
Hypotenuse
CAH - cos = Adjacent side
Hypotenuse
TOA - tan = Opposite side
Adjacent side
6 miles
Height
Army Daniel
WHY??WHY??
tan = Opposite side
Adjacent side
tan 60° (3mi) = h . (3mi)
3 mi
(tan 60°)(3 miles) = h
(0.866)(3) = h
h = 2.598 miles 3 miles
Height
h
Army Daniel
WHY??WHY??
tan = Opposite side
Adjacent side
tan 60° (3mi) = h . (3mi)
3 mi
(0.866 )(3 miles) = h
answer h = 2.598 miles
3 miles
Height
h= 2.598
Army Daniel
WHY??WHY??
tan = Opposite side
Adjacent side
tan 60° = h .
3 miles
(tan 60°)(3 miles) = h
(0.866)(3) = h
h = 2.598 miles 3 miles
Height
h
Army Daniel
WHY??WHY??
tan = Opposite side
Adjacent side
tan 60° = h .
3 miles
(tan 60°)(3 miles) = h
(0.866)(3) = h
h = 2.598 miles 3 miles
Height
h
Army Daniel
EXCELLENT!!!EXCELLENT!!!
You deserve a HAND!
Now, Let’s Work!!!
SOHCAHTOA!!!
Army Daniel
ASSIGNMENTASSIGNMENT
Class Asignment:
pp. 356-359 Problems #’s 1 – 40
Homework:
p. 360 – 361 #’s 3 – 51 multiples of 3
Army Daniel
ResourcesResources
Picture of Sohcahtoa:
[Devil’s Tower] http://www.animationfactory.com/free/nature/nature_page_aa.html