Pythagorean Theorem COSINE Calculations for Guide Right™ Guides DéPlaque Pythagorean Theorem COSINE 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

Correction based on the calculations from the Pythagorean Theorem To 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

A= cosine of 45º X 1.5 (0.707 X 1.5 mm = 1.06 mm

SOH stands for Sine equals Opposite over Hypotenuse. SOHCAHTOA A 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 CAH cos θ = _adjacent_ TOA tan θ = _opposite_ adjacent hypotenuse opposite side θ adjacent side

Find the values of sin θ, cos θ, and tan θ 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 cosθ = 4/5 = 0.8 tanθ = 3/4 = 0.75 adjacent side 4 5 Hypotenuse θ This triangle is oriented differently than the one shown in the SOHCAHTOA diagram, so make sure you know which sides are the opposite, adjacent, and hypotenuse.

Sine, Cosine and Tangent How is basic COSINE calculated? Sine, Cosine and Tangent Three Functions, but same idea. Right Triangle Sine, Cosine and Tangent are all based on a Right-Angled Triangle hypotenuse opposite side θ adjacent side

Sine, Cosine and Tangent Adjacent is always next to the angle And 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

sin(θ) = Opposite / Hypotenuse Cosine Function: Example: What is the sine of 35°? Sine Function: sin(θ) = Opposite / Hypotenuse Cosine Function: cos(θ) = Adjacent / Hypotenuse Tangent 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!

What are the sine, cosine and tangent of 45° ? 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 = 0.707 Cosine cos(45°) = 1 / 1.414 = 0.707 Tangent tan(45°) = 1 / 1 = 1 http://www.mathsisfun.com/sine-cosine-tangent.html