340 likes | 538 Views
SOH-CAH-TOA EAST OF JAVA. [Exploring Trigonometric Functions]. SOH-CAH-TOA means many things. “Hello” “Goodbye” “I love you” “Your slip is showing” “It’s Your turn to take out the trash!!!”. SOHCAHTOA Also Means: “Let’s do Trig!!. [SOH] Sine – Opposite – Hypotenuse
E N D
SOH-CAH-TOA EAST OF JAVA [Exploring Trigonometric Functions] Army Daniel
SOH-CAH-TOA means 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: “Let’s do Trig!! [SOH] Sine – Opposite – Hypotenuse [CAH] Cosine – Adjacent – Hypotenuse [TOA] Tangent – Opposite - Adjacent Army Daniel
First: A quick Geometry Review PARTS OF A RIGHT TRIANGLE OPPOSITE HYPOTENUSE ADJACENT Army Daniel
So, Sohcahtoa![…trans. “Let’s do Trig.!”] Army Daniel
We’ll break it into syllables. Army Daniel
SOH-CAH-TOA Army Daniel
SOH: SINE-OPP-HYP sin = opposite side hypotenuse OPPOSITE HYPOTENUSE ADJACENT Army Daniel
SOH-CAH-TOA Army Daniel
CAH: COSINE-ADJ-HYP cos = adjacent side hypotenuse OPPOSITE HYPOTENUSE ADJACENT Army Daniel
SOH-CAH-TOA Army Daniel
TOA: TAN-OPP-ADJ tan = opposite side adjacent OPPOSITE HYPOTENUSE ADJACENT Army Daniel
A QUICK REVIEW SOH - sin = Opposite side Hypotenuse CAH - cos = Adjacent side Hypotenuse TOA - tan = Opposite side Adjacent side Army Daniel
APPLICATIONS: Let’s solve a problem. Sohcahtoa! Army Daniel
Check for Understanding. Find sin = cos = tan = 5 3 4 Army Daniel
Check : Don’t Forget! Find sin = OPP HYP cos = ADJ HYP tan = OPP ADJ 3 ADJ 5 HYP 4 OPP Army Daniel
Check : ANSWERS Find sin = OPP = 4 HYP 5 cos = ADJ = 3 HYP 5 tan = OPP = 4 ADJ 3 3 ADJ 5 HYP 4 OPP Army Daniel
APPLICATIONS: Let’s try a different problem. Sohcahtoa! Army Daniel
Check for Understanding. Find x given: cos 60° = 0.5 x 60° 1 Army Daniel
Check for Understanding. Find x given: cos 60° = 0.5 And don’t forget SOH-CAH-TOA x 60° 1 Army Daniel
Check : ANSWER X = 2 How? x 60° 1 Army Daniel
Check : ANSWER X = 2 How? Use SOH – CAH - TOA cos 60° = .5 = ADJ = 1 HYP x .5x = 1 x = 2 x 60° 1 Army Daniel
APPLICATIONS: Let’s try a WORD problem! Sohcahtoa! Army Daniel
Find the Height of Mt. Sohcahtoa 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. Sohcahtoa What do we know? • = 60° Base = 6 miles = 3 miles 2 Height 6 miles Army Daniel
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? Height 6 miles Army Daniel
Which one? SOH - sin = Opposite side Hypotenuse CAH - cos = Adjacent side Hypotenuse TOA - tan = Opposite side Adjacent side Height 6 miles Army Daniel
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 Height h 3 miles Army Daniel
WHY?? tan = Opposite side Adjacent side tan 60°(3mi) = h .(3mi) 3 mi (0.866 )(3 miles) = h answer h = 2.598 miles Height h= 2.598 3 miles Army Daniel
WHY?? tan = Opposite side Adjacent side tan 60° = h . 3 miles (tan 60°)(3 miles) = h (0.866)(3) = h h = 2.598 miles Height h 3 miles Army Daniel
WHY?? tan = Opposite side Adjacent side tan 60° = h . 3 miles (tan 60°)(3 miles) = h (0.866)(3) = h h = 2.598 miles Height h 3 miles Army Daniel
EXCELLENT!!! You deserve a HAND! Now, Let’s Work!!! SOHCAHTOA!!! Army Daniel
Class Asignment: pp. 356-359 Problems #’s 1 – 40 Homework: p. 360 – 361 #’s 3 – 51 multiples of 3 ASSIGNMENT Army Daniel
Resources • Picture of Sohcahtoa: [Devil’s Tower] http://www.animationfactory.com/free/nature/nature_page_aa.html Army Daniel