Line 1: Line 1:
<div style="font-family: Verdana, sans-serif; font-size: 14px; text-align: justify; width: 80%; margin: auto; border: 1px solid #aaa; padding: 1em; text-align:right;">
+
<div style="font-family: Verdana, sans-serif; font-size: 14px; text-align: center; width: 70%; margin: auto; border: 1px solid #aaa; padding: 1em; text-align:center;">
 
{|
 
{|
 
|-
 
|-
|'''If you enjoy using this [[Collective_Table_of_Formulas|collective table of formulas]], please consider  [https://donate.purdue.edu/DesignateGift.aspx?allocation=017637&appealCode=11213&amount=25&allocationDescription=RheaProjectMimiBoutin donating to Project Rhea] or [[Donations | becoming a sponsor]].'''
+
|  
| [[Image:DonateNow.png]]
+
'''This [[Collective Table of Formulas|Collective table of formulas]] is proudly sponsored'''<br> '''by the [http://www.facebook.com/hkn.beta Nice Guys of Eta Kappa Nu].''' <br><br> Visit us at the HKN Lounge in EE24 for hot coffee and fresh bagels only $1 each!
|-
+
 
 +
| &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[Image:HKNlogo.jpg]]
 
|}
 
|}
</div>
+
</div>  
 
+
  
 
{|
 
{|

Revision as of 06:19, 5 April 2012

This Collective table of formulas is proudly sponsored
by the Nice Guys of Eta Kappa Nu.

Visit us at the HKN Lounge in EE24 for hot coffee and fresh bagels only $1 each!

                                         HKNlogo.jpg
Trigonometric Identities
Basic Definitions
Definition of tangent $ \tan \theta = \frac{\sin \theta}{\cos\theta} $
Definition of cotangent $ \cot \theta = \frac{\cos \theta}{\sin\theta} \ $ credit
Definition of secant $ \sec \theta = \frac{1}{\cos \theta} \ $
Definition of cosecant $ \csc \theta = \frac{1}{\sin \theta} \ $
Definition of versed sine (versine) $ \text{versin } \theta = 1- \cos \theta \ $
Definition of versed cosine (versine) $ \text{vercosin } \theta = 1+ \cos \theta \ $
Definition of coversed sine (coversine) $ \text{coversin } \theta = \text{cvs } \theta = 1- \sin \theta \ $
Definition of coversed cosine (covercosine) $ \text{covercosin } \theta = 1+ \sin \theta \ $
Definition of haversed sine (haversine) $ \text{haversin } \theta = \frac{1- \cos \theta}{2} $
Definition of haversed cosine (havercosine) $ \text{havercosin } \theta = \frac{1+ \cos \theta}{2} $
Definition of hacoversed sine (hacoversin) $ \text{hacoversin } \theta = \frac{1 - \sin \theta}{2} $
Definition of hacoversed cosine (hacovercosin) $ \text{hacovercosin } \theta = \frac{1 + \sin \theta}{2} $
Definition of exterior secant (exsec) $ \text{exsec } \theta = \sec \theta - 1 \ $
Definition of exterior cosecant (excosec) $ \text{excosec } \theta = \csc \theta - 1 \ $
Definition of chord (crd) $ \text{crd } \theta = 2 \sin(\frac{\theta}{2}) $
Pythagorean identity and other related identities
Pythagorean identity $ \cos^2 \theta+\sin^2 \theta =1 \ $
$ \sin^2 \theta = 1-\cos^2 \theta \ $
$ \cos^2 \theta = 1-\sin^2 \theta \ $
$ \sec^2 \theta = 1+\tan^2 \theta \ $
$ \csc^2 \theta = 1+\cot^2 \theta \ $
please continue place formula here
Half-Angle Formulas
Half-angle for sine $ \sin \frac{\theta}{2} = \pm \sqrt{ \frac{1-\cos \theta}{2} } \ $
Half-angle for cosine $ \cos \frac{\theta}{2} = \pm \sqrt{ \frac{1+\cos \theta}{2} } \ $
Half-angle for tangent $ \tan \frac{\theta}{2} = \csc \theta - \cot \theta \ $
Half-angle for tangent $ \tan \frac{\theta}{2} =\pm\sqrt{\frac{1-\cos \theta}{ 1+\cos \theta }} \ $
Half-angle for tangent $ \tan \frac{\theta}{2} =\frac{\sin \theta}{ 1+\cos \theta } \ $
Half-angle for tangent $ \tan \frac{\theta}{2} =\frac{1-\cos \theta}{ \sin \theta } \ $
Half-angle for cotangent $ \cot \frac{\theta}{2} = \csc \theta + \cot \theta $
Half-angle for cotangent $ \cot \frac{\theta}{2} = \frac{1 + \cos \theta}{\sin \theta} $
Half-angle for cotangent $ \cot \frac{\theta}{2} = \pm \sqrt{1 + \cos \theta \over 1 - \cos \theta} $
Half-angle for cotangent $ \cot \frac{\theta}{2} = \frac{\sin \theta}{1 - \cos \theta} $
Double-Angle Formulas
double-angle for sine $ \sin 2 \theta = 2 \sin \theta \cos \theta \ $ credit
double-angle for sine $ \sin 2 \theta = \frac{ 2 \tan \theta}{1+ \tan^2 \theta } \ $
double-angle for cosine $ \cos 2 \theta =\cos^2 \theta - \sin^2 \theta \ $
double-angle for cosine $ \cos 2 \theta =2 \cos^2 \theta - 1 \ $
double-angle for cosine $ \cos 2 \theta =1- 2 \sin^2 \theta \ $
double-angle for cosine $ \cos 2 \theta =\frac{1- \tan^2 \theta}{ 1+\tan^2 \theta } \ $
double-angle for tangent $ \tan 2\theta = \frac{2 \tan \theta} {1 - \tan^2 \theta}\, $
double-angle for cotangent $ \cot 2\theta = \frac{\cot^2 \theta - 1}{2 \cot \theta}\, $
Triple-Angle Formulas
triple-angle for sine $ \begin{align}\sin 3\theta & = 3 \cos^2\theta \sin\theta - \sin^3\theta \\ & = 3\sin\theta - 4\sin^3\theta \end{align} $
triple-angle for cosine $ \begin{align}\cos 3\theta & = \cos^3\theta - 3 \sin^2 \theta\cos \theta \\ & = 4 \cos^3\theta - 3 \cos\theta\end{align} $
triple-angle for tangent $ \tan 3\theta = \frac{3 \tan\theta - \tan^3\theta}{1 - 3 \tan^2\theta} $
tripe-angle for cotangent $ \cot 3\theta = \frac{3 \cot\theta - \cot^3\theta}{1 - 3 \cot^2\theta} $
Angle sum and difference identities
Sine $ \sin \left( \theta\pm \alpha \right)=\sin \theta \cos \alpha \pm \cos \theta \sin \alpha $
Cosine $ \cos \left(\theta\pm \alpha \right)= \cos \theta \cos \alpha \mp \sin \theta \sin \alpha $
Tangent $ \tan \left(\theta\pm \alpha \right)= \frac {\tan \theta \pm \tan \alpha}{1 \mp \tan \theta \tan \alpha} $
Arcsine $ \arcsin\alpha \pm \arcsin\beta = \arcsin(\alpha\sqrt{1-\beta^2} \pm \beta\sqrt{1-\alpha^2}) $
Arccosine $ \arccos\alpha \pm \arccos\beta = \arccos(\alpha\beta \mp \sqrt{(1-\alpha^2)(1-\beta^2)}) $
Arctangent $ \arctan\alpha \pm \arctan\beta = \arctan\left(\frac{\alpha \pm \beta}{1 \mp \alpha\beta}\right) $

Back to Collective Table

Alumni Liaison

Recent Math PhD now doing a post-doctorate at UC Riverside.

Kuei-Nuan Lin