Difference between revisions of "Comments:LaTeX-code for the most common formulas"

From GeoGebra Manual
Jump to: navigation, search
m (remove old Java / HTML5 reference)
 
(33 intermediate revisions by 10 users not shown)
Line 1: Line 1:
''If you have somewhere a very long formula, please share it with us. This will save time for everybody!''
+
{{DISPLAYTITLE:LaTeX code for the most common formulas}}
==Design-Tip==
+
If you have somewhere a very long formula, please share it with us. This will save time for everybody!'' Just edit this page and paste you code at inside the input-box, if you don't know how to use the wiki-code correctly.
* A space before the formula leeds to the box around the line.  
+
==How to use the formulas==
* Don't hesitate it is not looking so good. That can be done by anybody else.  
+
Just copy the text from the column '''LaTex Input''' into your text-object input-box. If the formula should be dynamic you need to insert the object instead of the variables that are used here.
* An easy solution to get the same look is to copy the lines of an other formula for you formula.
+
==Preview==
 +
Examples in GeoGebra [https://www.geogebra.org/m/jvXBfFY6 https://www.geogebra.org/m/jvXBfFY6]
  
==How to use the formulas==
+
==Useful Formulas==
Just copy the text in the dotted box into you text-input-box. If the formula should be dynamic you need to insert the object at the place of the variable that is used here.
+
<small>
 +
{| class="pretty"
 +
! Usage !! LaTex Input !! LaTex Output
 +
|-
 +
| Square-root symbol
 +
| \sqrt{x}
 +
| <math>\sqrt{x}</math>
 +
|-
 +
| Fractions
 +
| \frac{a}{b+c}
 +
| <math>\frac{a}{b+c}</math>
 +
|-
 +
| \left( and \right) for large brackets
 +
| \left( \frac{a}{b} \right) ^{2}
 +
| <math>\left( \frac{a}{b} \right) ^{2}</math>
 +
|-
 +
| Use \textcolor for color
 +
| x^{\textcolor{#FF00FF}{2}}
 +
|
 +
|-
 +
| Use \cr for a line break
 +
| x=3 \cr y=2
 +
| <math>\begin{array}  x=3 \\ y=2 \end{array}</math>
 +
|-
 +
| Use \text{ } to mix text and expressions
 +
| \text{Roots of }ax^2 + bx + c= 0\text{ are }x = \frac {-b \pm \sqrt {b^2 - 4ac}}{2a}
 +
| <math>\text{Roots of }ax^2 + bx + c= 0 \text{ are }</math><br><math>x = \frac {-b \pm \sqrt {b^2 - 4ac}}{2a}</math>
 +
|-
 +
| Slope for  a straight line
 +
| m=\frac{y_2-y_1}{x_2-x_1}
 +
| <math>m=\frac{y_2-y_1}{x_2-x_1}</math>
 +
|-
 +
| Slope for  a straight line (2)
 +
| m= \frac{Δy}{Δx}=\frac{y_A-y_B}{x_A-x_B}
 +
| <math>m= \frac{Δy}{Δx}=\frac{y_A-y_B}{x_A-x_B}</math>
 +
|-
 +
| Compound Interest
 +
| Amount = Principal \cdot \left( 1 + \frac {rate}{periods}  \right)  ^ {time  \cdot  periods}
 +
|<math>Amount = Principal \cdot \left( 1 + \frac {rate}{periods}  \right)  ^ {time \cdot periods}</math>
 +
|-
 +
| Quadratic Equation
 +
| a x^2 + b x + c = 0
 +
| <math>a x^2 + b x +  c  =  0</math>
 +
|-
 +
| Simplified Quadratic Equation
 +
| x^2 + p x + q = 0
 +
| <math>x^2 +  p x  +  q  =  0</math>
 +
|-
 +
| Vertex Form
 +
|  f(x) =  a(x - h)^2 + k
 +
| <math> f(x)  =  a(x  -  h)^2 +  k</math>
 +
|-
 +
| Factored Form
 +
| f(x) = (x + a)(x + b)
 +
| <math>f(x) = (x + a)(x + b)</math>
 +
|-
 +
| Quadratic Formula
 +
| x  =  \frac {-b  \pm  \sqrt {b^2  -  4ac}}{2a}
 +
| <math>x  =  \frac {-b  \pm  \sqrt {b^2  -  4ac}}{2a}</math>
 +
|-
 +
| Quadratic Formula
 +
| x_{1/2}  =  \frac {-b  \pm  \sqrt {b^2  -  4ac}}{2a}
 +
| <math>x_{1/2}  =  \frac {-b  \pm  \sqrt {b^2  -  4ac}}{2a}</math>
 +
|-
 +
| Quadratic Formula for Simplified Quadratic Equation
 +
| x_{1/2}  =  - \frac{p}{2}{  \pm  \sqrt {\left( \frac{p}{2} \right)^2  -  q}}
 +
| <math>x_{1/2}  =  - \frac{p}{2}{  \pm  \sqrt {\left( \frac{p}{2} \right)^2  -  q}}</math>
 +
|-
 +
| Quadratic Formula for Simplified Quadratic Equation
 +
| x_{1/2}  =  - \frac{p}{2}{  \pm  \sqrt {\left( \frac{p}{2} \right)^2  -  q}}
 +
| <math>x_{1/2}  =  - \frac{p}{2}{  \pm  \sqrt { \frac{p^2}{4}  -  q}}</math>
 +
|-
 +
| Cubic Equation
 +
| a x^3  +  b x^2  +  c x  +  d  =  0
 +
| <math>a x^3  +  b x^2  +  c x  +  d  =  0</math>
 +
|-
 +
| Basic Trigonometry Forms
 +
| \sin A = \frac {opp}{hyp} = \frac {a}{c} = (a/c)
 +
| <math>\sin A = \frac {opp}{hyp} = \frac {a}{c} = (a/c)</math>
 +
|-
 +
|
 +
| f(x)  =  a  \sin  b (x  -  h)  +  k
 +
| <math>f(x)  =  a  \sin  b (x  -  h)  +  k</math>
 +
|-
 +
|
 +
| f(x)  =  a  sin  (B x + C) + k
 +
| <math>f(x)  =  a  \sin  (B x + C) + k</math>
 +
|-
 +
|
 +
| b (x  -  h)  = B  \left( x  -  \frac {-C}{B} \right)
 +
| <math>b (x  -  h)  = B  \left( x  -  \frac {-C}{B} \right)</math>
 +
|-
 +
|
 +
| h  = \frac {-C}{B}
 +
| <math>h  = \frac {-C}{B}</math>
 +
|-
 +
| Limit (corrected to work in HTML5 as well as Java)
 +
| \lim_{x \to \infty} \left( \frac{1}{x} \right)
 +
| <math>\lim_{x \to \infty} \left( \frac{1}{x} \right)</math>
 +
|-
 +
| Distance Formula
 +
| \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}
 +
| <math>\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}</math>
 +
|}
  
==Formulas==
+
==Text formatting==
* '''Slope for  a straight line:'''
+
<small>
m=\frac{y_2-y_1}{x_2-x_1}
+
{| class="pretty"
::<math>m=\frac{y_2-y_1}{x_2-x_1}</math>
+
! Usage !! LaTex Input !! LaTex Output
* ""Quadratic Equation:""
+
|-
a x^2\; +\; b x\; +\; c\; =\; 0
+
| Text with spacing
::<math>a x^2\; +\; b x\; +\; c\; =\; 0</math>
+
| \text{some words with spaces}
*""Quadratic Formula::""
+
| <math>\text{some words with spaces}</math>
x\; =\; \frac {-b\; \pm\; \sqrt {b^2\; -\; 4ac}}{2a}
+
|-
::<math>x\; =\; \frac {-b\; \pm\; \sqrt {b^2\; -\; 4ac}}{2a}</math>
+
| Italic text
*""Cubic Equation::""
+
| \mathit{italic text}
a x^3\; +\; b x^2\; +\; c x\; +\; d\; =\; 0
+
| <math>\mathit{italic text}</math>
::<math>a x^3\; +\; b x^2\; +\; c x\; +\; d\; =\; 0</math>
+
|-
*""Basic Trigonometry::""
+
| Bold text
sin A = \frac {opp}{hyp} = \frac {a}{c} = (a/c)
+
| \mathbf{bold text}
::<math>sin A = \frac {opp}{hyp} = \frac {a}{c} = (a/c)</math>
+
| <math>\mathbf{bold text}</math>
*""Vertex Form::""
+
|-
f(x)\; =\; a(x\; -\; h)^2\; +\; k
+
</small>
::<math>f(x)\; =\; a(x\; -\; h)^2\; +\; k</math>
 
*""Factored Form::""
 
f(x)\; =\; (x\; +\; a)\;(x\; +\; b)
 
::<math>f(x)\; =\; (x\; +\; a)\;(x\; +\; b)</math>
 

Latest revision as of 10:54, 11 January 2020

If you have somewhere a very long formula, please share it with us. This will save time for everybody! Just edit this page and paste you code at inside the input-box, if you don't know how to use the wiki-code correctly.

How to use the formulas

Just copy the text from the column LaTex Input into your text-object input-box. If the formula should be dynamic you need to insert the object instead of the variables that are used here.

Preview

Examples in GeoGebra https://www.geogebra.org/m/jvXBfFY6

Useful Formulas

Usage LaTex Input LaTex Output
Square-root symbol \sqrt{x} \sqrt{x}
Fractions \frac{a}{b+c} \frac{a}{b+c}
\left( and \right) for large brackets \left( \frac{a}{b} \right) ^{2} \left( \frac{a}{b} \right) ^{2}
Use \textcolor for color x^{\textcolor{#FF00FF}{2}}
Use \cr for a line break x=3 \cr y=2 \begin{array} x=3 \\ y=2 \end{array}
Use \text{ } to mix text and expressions \text{Roots of }ax^2 + bx + c= 0\text{ are }x = \frac {-b \pm \sqrt {b^2 - 4ac}}{2a} \text{Roots of }ax^2 + bx + c= 0 \text{ are }
x = \frac {-b \pm \sqrt {b^2 - 4ac}}{2a}
Slope for a straight line m=\frac{y_2-y_1}{x_2-x_1} m=\frac{y_2-y_1}{x_2-x_1}
Slope for a straight line (2) m= \frac{Δy}{Δx}=\frac{y_A-y_B}{x_A-x_B} m= \frac{Δy}{Δx}=\frac{y_A-y_B}{x_A-x_B}
Compound Interest Amount = Principal \cdot \left( 1 + \frac {rate}{periods} \right) ^ {time \cdot periods} Amount = Principal \cdot \left( 1 + \frac {rate}{periods} \right) ^ {time \cdot periods}
Quadratic Equation a x^2 + b x + c = 0 a x^2 + b x + c = 0
Simplified Quadratic Equation x^2 + p x + q = 0 x^2 + p x + q = 0
Vertex Form f(x) = a(x - h)^2 + k f(x) = a(x - h)^2 + k
Factored Form f(x) = (x + a)(x + b) f(x) = (x + a)(x + b)
Quadratic Formula x = \frac {-b \pm \sqrt {b^2 - 4ac}}{2a} x = \frac {-b \pm \sqrt {b^2 - 4ac}}{2a}
Quadratic Formula x_{1/2} = \frac {-b \pm \sqrt {b^2 - 4ac}}{2a} x_{1/2} = \frac {-b \pm \sqrt {b^2 - 4ac}}{2a}
Quadratic Formula for Simplified Quadratic Equation x_{1/2} = - \frac{p}{2}{ \pm \sqrt {\left( \frac{p}{2} \right)^2 - q}} x_{1/2} = - \frac{p}{2}{ \pm \sqrt {\left( \frac{p}{2} \right)^2 - q}}
Quadratic Formula for Simplified Quadratic Equation x_{1/2} = - \frac{p}{2}{ \pm \sqrt {\left( \frac{p}{2} \right)^2 - q}} x_{1/2} = - \frac{p}{2}{ \pm \sqrt { \frac{p^2}{4} - q}}
Cubic Equation a x^3 + b x^2 + c x + d = 0 a x^3 + b x^2 + c x + d = 0
Basic Trigonometry Forms \sin A = \frac {opp}{hyp} = \frac {a}{c} = (a/c) \sin A = \frac {opp}{hyp} = \frac {a}{c} = (a/c)
f(x) = a \sin b (x - h) + k f(x) = a \sin b (x - h) + k
f(x) = a sin (B x + C) + k f(x) = a \sin (B x + C) + k
b (x - h) = B \left( x - \frac {-C}{B} \right) b (x - h) = B \left( x - \frac {-C}{B} \right)
h = \frac {-C}{B} h = \frac {-C}{B}
Limit (corrected to work in HTML5 as well as Java) \lim_{x \to \infty} \left( \frac{1}{x} \right) \lim_{x \to \infty} \left( \frac{1}{x} \right)
Distance Formula \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2} \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}

Text formatting

Usage LaTex Input LaTex Output
Text with spacing \text{some words with spaces} \text{some words with spaces}
Italic text \mathit{italic text} \mathit{italic text}
Bold text \mathbf{bold text} \mathbf{bold text}
© 2022 International GeoGebra Institute