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We already know so much about Vectors like… •What is a Vector? •What is a Scalar? •What are the parts of a Vector? •And wait…there’s more Vector Components Any vector can be broken up into two perpendicular components that lie along the x axis and along the y axis. -You can think of an individual component of a vector as the shadow it would cast on either the x axis or the y axis. y component -We call these the x and y components of a vector. x component y component also y component Components x component Island of SOH-CAH-TOA [Exploring Trigonometric Functions] SOHCAHTOA Also Means: “Let’s do Trig!! But….What is Trigonometry! Trigonometry, or trig are sets of useful ratios used for finding various parts of right triangles. NOW…”Lets do Trig!” SOH-CAH-TOA [SOH] Sine – Opposite – Hypotenuse [CAH] Cosine – Adjacent – Hypotenuse [TOA] Tangent – Opposite - Adjacent First: A quick Geometry Review PARTS OF A RIGHT TRIANGLE O P P O S I T E HYPOTENUSE ADJACENT So, Sohcahtoa! […trans. “Let’s do Trig.!”] We’ll break it into syllables. SOH-CAH-TOA SOH: SINE-OPP-HYP sin = opposite side hypotenuse O P P O S I T E HYPOTENUSE ADJACENT CAH-TOA SOH- CAH: COSINE-ADJ-HYP cos = adjacent side hypotenuse O P P O S I T E HYPOTENUSE ADJACENT TOA SOH-CAH- TOA: TAN-OPP-ADJ tan = opposite side adjacent O P P O S I T E HYPOTENUSE ADJACENT A QUICK REVIEW SOH Sin Opposite Hypotenuse CAH Cosine Adjacent Hypotenuse TOA Tangent Opposite Adjacent APPLICATIONS: Let’s solve a simple problem. Sohcahtoa! The natives launch a coconut at 25 m/s at an angle of 30 with the horizontal. What are the horizontal and vertical components of the velocity? Vertical component Y- component 30 Horizontal component X- component The solution! 30 Vertical component Y- component opposite= sin* hypotenuse = sin 30 (25 m/s) = 0.5 (25 m/s) = 12.5 m/s Horizontal component X- component adjacent = cos * hypotenuse = cos 30 (25 m/s) = 0.866 (25 m/s) = 21.7 m/s APPLICATIONS: Let’s try a WORD problem! Sohcahtoa! Find the Height of Mt. Sohcahtoa The volcano is rumbling. The Sohcahtoans need to sacrifice a Physics Student. They know the base of the mountain is 6 Km wide. The angle formed from the base to the top is 60°. How tall is the mountain? [Use your calculator!!!] Find the Height of Mt. Sohcahtoa What do we know? = 60° Base = 6 Km = 3 Km 2 H e i g h t 6 Km What else do know? sin = Opposite side Hypotenuse CAH - cos = Adjacent side Hypotenuse tan = Opposite side Adjacent side SOH - TOA - H e i g h t Which one should we use? 6 Km WHY?? tan = Opposite side Adjacent side tan 60° = h _ 3 Km H e i g h t 3 Km h What if I want to find an angle? Here we know the opposite side and the hypotenuse. So we will use the sin function 20 cm Sin-1(opp/hyp) = = 36.87 degrees - this is called the inverse sin function Back to the Island of SOHCAHTOA The crafty physics student wants to escape death by volcano and land behind the angry SOHCAHTOANS. He builds a slide from the top of the Volcano (5.2 Km high) to land 7 Km from the base of the volcano. What are the angles the slide will make with the volcano and the ground?