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7 use of pythagorean theorem cosine calculation for guide right

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Guide Right Surgical Guide System: fabrication and correction of Diagnostic & Surgical Guides with 2D & 3D X-ray Images

Guide Right Surgical Guide System: fabrication and correction of Diagnostic & Surgical Guides with 2D & 3D X-ray Images


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  • 1. DéPlaque Pythagorean TheoremCOSINE Calculations for Guide Right™ Guides The cosine of 45 is recommended for Guide Right corrections BECAUSE rotating the offset guide post half way between 2 adjacent planes (90 apart) is 45 . 2.2013
  • 2. Correction based on the calculations from the Pythagorean TheoremTo move the position of the guide sleeve 1.4 mm both mesially & buccally: ► use a 3 mm X 1.5 mm offset guide post ► and direct the offset 45º facially and buccally. Cosine: 1.5 mm X 0.71 = 1.06 mm see Powerpoint > Use of Pythagorean Theorem in # 9 Single Implant Case
  • 3. A= cosine of 45º X 1.5(0.707 X 1.5 mm = 1.06 mm
  • 4. SOHCAHTOAA way of remembering how to compute the sine, cosine, and tangent of an angle. SOH stands for Sine equals Opposite over Hypotenuse. CAH stands for Cosine equals Adjacent over Hypotenuse. TOA stands for Tangent equals Opposite over Adjacent. SOH sin θ = _opposite_ hypotenuse hypotenuse CAH cos θ = _adjacent_ opposite side hypotenuse θ TOA tan θ = _opposite_ adjacent adjacent side
  • 5. 3 EXAMPLE Find the values of sin θ, cos θ, and tan θ in the right triangle shown. 4 5 θ 3 opposite side ANSWER sin θ = 3/5 = 0.6 adjacent side cosθ = 4/5 = 0.8 tanθ = 3/4 = 0.75 4 5This triangle is oriented differently than the θone shown in the SOHCAHTOAdiagram, so make sure you know whichsides are the opposite, adjacent, andhypotenuse.
  • 6. How is basic COSINE calculated? Sine, Cosine and Tangent Three Functions, but same idea. Right TriangleSine, Cosine and Tangent are all based on a Right-Angled Triangle opposite side θ adjacent side
  • 7. Adjacent is always next to the angleAnd Opposite is opposite the angle Sine, Cosine and Tangent The three main functions in trigonometry are Sine, Cosine and Tangent. They are often shortened to sin, cos and tan. To calculate them: Divide the length of one side by another side ... but you must know which sides! For a triangle with an angle θ, the functions are calculated this way: examples follow
  • 8. Example: What is the sine of 35 ? Sine Function: sin(θ) = Opposite / HypotenuseCosine Function: cos(θ) = Adjacent / HypotenuseTangent Function: tan(θ) = Opposite / Adjacent Using this triangle (lengths are only to one decimal place): sin(35 ) = Opposite / Hypotenuse = 2.8 / 4.9 = 0.57... Good calculators have sin, cos and tan on them, to make it easy for you. Just put in the angle and press the button. But you still need to remember what they mean!
  • 9. Example: What are the sine, cosine and tangent of 45 ? Used in Guide Right™ Surgical guide calculations The classic 45 triangle has two sides of 1 and a hypotenuse of √(2 Sine sin(45 ) = 1 / 1.414 = 0.707Cosine cos(45 ) = 1 / 1.414 = 0.707Tangent tan(45 ) = 1 / 1 = 1 http://www.mathsisfun.com/sine-cosine-tangent.html