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 Army Daniel

SOH-CAH-TOA Army Daniel

TOA: TAN-OPP-ADJ tan  = opposite side adjacent OPPOSITE HYPOTENUSE Army Daniel

A QUICK REVIEW SOH - sin  = Opposite side Hypotenuse CAH - cos  = Adjacent side 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 3 ADJ tan  = OPP ADJ 3 ADJ 5 HYP 4 OPP Army Daniel

Check : ANSWERS Find sin  = OPP = 4 HYP 5 cos  = ADJ = 3 3 ADJ 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 How? Use SOH – CAH - TOA cos 60° = .5 = ADJ = 1 HYP x x 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? Height 6 miles SOH - sin  = Opposite side Hypotenuse CAH - cos  = Adjacent side TOA - tan  = Opposite side Adjacent side Which one should we use? Height 6 miles Army Daniel

Which one? Height 6 miles SOH - sin  = Opposite side Hypotenuse CAH - cos  = Adjacent side TOA - tan  = Opposite side Adjacent side Height 6 miles Army Daniel

WHY?? Height h 3 miles 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?? Height h= 2.598 3 miles 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?? Height h 3 miles 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?? Height h 3 miles 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

You deserve a HAND! Now, Let’s Work!!! SOHCAHTOA!!! EXCELLENT!!! Army Daniel

ASSIGNMENT Class Asignment: pp. 356-359 Problems #’s 1 – 40 Homework: p. 360 – 361 #’s 3 – 51 multiples of 3 Army Daniel

Resources Picture of Sohcahtoa: [Devil’s Tower] http://www.animationfactory.com/free/nature/nature_page_aa.html Army Daniel