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Army Daniel SOH-CAH-TOA EAST OF JAVA [Exploring Trigonometric Functions]

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Army Daniel SOH-CAH-TOA means many things Hello Goodbye I love you Your slip is showing Its Your turn to take out the trash!!!

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Army Daniel SOHCAHTOA Also Means: Lets do Trig!! [SOH]Sine – Opposite – Hypotenuse [CAH]Cosine – Adjacent – Hypotenuse [TOA]Tangent – Opposite - Adjacent

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Army Daniel First: A quick Geometry Review PARTS OF A RIGHT TRIANGLE OPPOSITEOPPOSITE ADJACENT HYPOTENUSE

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Army Daniel So, Sohcahtoa! […trans. Lets do Trig.!]

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Army Daniel Well break it into syllables.

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Army Daniel SOH -CAH-TOA

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Army Daniel SOH: SINE-OPP-HYP sin = opposite side hypotenuse OPPOSITEOPPOSITE ADJACENT HYPOTENUSE

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Army Daniel SOH- CAH -TOA SOH- CAH -TOA

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Army Daniel CAH: COSINE-ADJ-HYP cos = adjacent side hypotenuse OPPOSITEOPPOSITE ADJACENT HYPOTENUSE

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Army Daniel SOH-CAH- TOA SOH-CAH- TOA

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Army Daniel TOA: TAN-OPP-ADJ tan = opposite side adjacent OPPOSITEOPPOSITE ADJACENT HYPOTENUSE

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Army Daniel A QUICK REVIEW SOH - sin = Opposite side Hypotenuse CAH -cos = Adjacent side Hypotenuse TOA -tan = Opposite side Adjacent side

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Army Daniel APPLICATIONS: Lets solve a problem. Sohcahtoa!

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Army Daniel Check for Understanding. Find sin = cos = tan = 3 4 5

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Army Daniel Check : Dont Forget! Find sin = OPP HYP cos = ADJ HYP tan = OPP ADJ 3ADJ3ADJ 4 OPP 5 HYP

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Army Daniel Check : ANSWERS Find sin = OPP = 4 HYP 5 cos = ADJ = 3 HYP 5 tan = OPP = 4 ADJ 3 3ADJ3ADJ 4 OPP 5 HYP

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Army Daniel APPLICATIONS: Lets try a different problem. Sohcahtoa!

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Army Daniel Check for Understanding. Find x given: cos 60° = ° x 1

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Army Daniel Check for Understanding. Find x given: cos 60° = 0.5 And dont forget SOH-CAH-TOA 60° x 1

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Army Daniel Check : ANSWER X = 2 How? 60° x 1

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Army Daniel Check : ANSWER X = 2 How? Use SOH – CAH - TOA cos 60° =.5 = ADJ = 1 HYP x.5x = 1 x = 2 60° x 1

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Army Daniel APPLICATIONS: Lets try a WORD problem! Sohcahtoa!

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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!!!]

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Army Daniel Find the Height of Mt. Sohcahtoa What do we know? = 60° Base = 6 miles = 3 miles 2 6 miles HeightHeight

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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? 6 miles HeightHeight

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

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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 = miles 3 miles HeightHeight h

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Army Daniel WHY?? tan = Opposite side Adjacent side tan 60° (3mi) = h. (3mi) 3 mi (0.866 )(3 miles) = h answer h = miles 3 miles HeightHeight h= 2.598

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Army Daniel WHY?? tan = Opposite side Adjacent side tan 60° = h. 3 miles (tan 60°)(3 miles) = h (0.866)(3) = h h = miles 3 miles HeightHeight h

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Army Daniel WHY?? tan = Opposite side Adjacent side tan 60° = h. 3 miles (tan 60°)(3 miles) = h (0.866)(3) = h h = miles 3 miles HeightHeight h

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Army Daniel EXCELLENT!!! You deserve a HAND! Now, Lets Work!!! SOHCAHTOA!!!

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

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Army Daniel Resources Picture of Sohcahtoa: [Devils Tower] ture/nature_page_aa.html ture/nature_page_aa.html

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