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Basics of Trigonometry Click triangle to continue What is Trigonometry? Right Angled Triangles Sine Cosine and Tangent Pythagorean Theorem What is Trigonometry? • Trigonometry (from Greek trigonon "triangle" + metron "measure") • Trig is all about triangles! • The three sides of the triangle are labeled • Hypotenuse • Adjacent • Opposite Right Angled Triangles • We can find any angle of a right triangle as long as we have the lengths of 2 sides. • We can find the length of any side of a right triangle as long as we have at least one angle and side. • If given one angle, add 90 and subtract sum from 180 to find the missing angle of the triangle (HELPFUL HINTS) • *SOH CAH TOA can only be used for right triangles* • *The hypotenuse is ALWAYS across from the right angle* Sine, Cosine, and Tangent • We use these three trig functions to find the angles and sides of right triangles. • For short we use the term SOH-CAH-TOA • SOH: Sin = opposite/hypotenuse • CAH: Cos = adjacent/hypotenuse • TOA: Tan = opposite/adjacent • Lets look at some examples A.) Example of a triangle with a length and angle • Step 1: The two sides we are using are Adjacent (h) and Hypotenuse (1000). • Step 2: SOH-CAH-TOA tells us to use Cosine. • Step 3: Put our values into the Cosine equation: cos 60° = Adj/ Hyp cos 60° = h / 1000 • Step 4 Solve: Solving The Problem • Find the height of the plane • (h = height) • Cos 60° = h/1000 so by using basic algebra, we know to plug 1000cos(60) into the calculator to find the height of the plane! • Cos 60° = h/1000 • 1000cos(60°) = h • Height = 500 B.) Example of a triangle with 2 Side Lengths • Step 1: The two sides we know are Opposite (300) and Adjacent(400). • Step 2: SOH-CAH-TOA tells us we must use Tangent. • Step 3: Calculate Opposite/Adjacent = 300/400 = 0.75 • Step 4: Find the angle from your calculator using tan-1 • We use the inverse of Sine, Cosine, and Tangent to find missing angles Solving The Problem • Find the angle of elevation • You can solve this problem two different ways • Tan-1 (300/400) = answer • OR • 300/400 = 0.75 so Tan-1 (0.75) = answer • The answer is 36.87° Pythagorean Theorem • When we are trying to find just the sides of the triangle, we use the Pythagorean theorem. • This equation only works for right triangles! • Equation: a2 + b2 = c2 • Remember that “c” is the hypotenuse • Can you find the answer to “c”? How to Solve for “C” (Steps) • Step 1: write out equation a2 + b2 = c2 • Step 2: plug in numbers 52 + 122 = c2 • Step 3: square the numbers 25 + 144 = c2 • Step 4: add like terms 169 = c2 • Step 5: take the square root c = √169 • Step 6: final answer c = 13 QUIZ! • What two sides would we use for a problem dealing with Cosine? • A.) opposite/hypotenuse • B.) opposite/adjacent • C.) adjacent/hypotenuse A.) opposite/hypotenuse Sorry! Try again • Opposite/Hypotenuse is used for Sine • Remember *SOH-CAH-TOA* B.) Opposite/Adjacent Sorry! Try again • Opposite/Adjacent is used for Tangent • Remember *SOH-CAH-TOA* C.) Adjacent/Hypotenuse Great Job! You got it! • Adjacent/Hypotenuse is used for Cosine You have completed the lesson! • Please click here to go back to the beginning