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°.

DéPlaque

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

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.

hypotenuse

opposite side

adjacent side

θ

SOH sin θ = _opposite_

hypotenuse

CAH cos θ = _adjacent_

hypotenuse

TOA tan θ = _opposite_

adjacent

3

5

4

θ

EXAMPLE

Find the values of sin θ, cos θ, and tan θ

in the right triangle shown.

5 4

θ

3 opposite side

adja

cent s

ide

ANSWER

sin θ = 3/5 = 0.6

cosθ = 4/5 = 0.8

tanθ = 3/4 = 0.75

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.

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

opposite side

adjacent side

θ

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

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!

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

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