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| align="right" style="padding-right: 1em;" |Half-angle for cosine | | align="right" style="padding-right: 1em;" |Half-angle for cosine | ||
| − | |<math> \ | + | |<math> \cos \frac{\theta}{2} = \pm \sqrt{ \frac{1+\cos \theta}{2} } \ </math> |
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" |Half-angle for tangent | ||
| + | |<math> \tan \frac{\theta}{2} = \csc \theta - \cot \theta \ </math> | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" |Half-angle for tangent | ||
| + | |<math> \tan \frac{\theta}{2} =\pm\sqrt{\frac{1-\cos \theta}{ 1+\cos \theta }} \ </math> | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" |Half-angle for tangent | ||
| + | |<math> \tan \frac{\theta}{2} =\frac{\sin \theta}{ 1+\cos \theta } \ </math> | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" |Half-angle for tangent | ||
| + | |<math> \tan \frac{\theta}{2} =\frac{1-\cos \theta}{ \sin \theta } \ </math> | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" | Half-angle for cotangent | ||
| + | | <math>\cot \frac{\theta}{2} = \csc \theta + \cot \theta </math> | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" | Half-angle for cotangent | ||
| + | | <math>\cot \frac{\theta}{2} = \frac{1 + \cos \theta}{\sin \theta} </math> | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" | Half-angle for cotangent | ||
| + | | <math>\cot \frac{\theta}{2} = \pm \sqrt{1 + \cos \theta \over 1 - \cos \theta} </math> | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" | Half-angle for cotangent | ||
| + | | <math>\cot \frac{\theta}{2} = \frac{\sin \theta}{1 - \cos \theta} </math> | ||
|- | |- | ||
| align="right" style="padding-right: 1em;" | please continue | | align="right" style="padding-right: 1em;" | please continue | ||
Revision as of 08:35, 22 October 2010
| Trigonometric Identities | |
|---|---|
| Basic Definitions | |
| Definition of tangent | $ \tan \theta = \frac{\sin \theta}{\cos\theta} $ credit |
| 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{ver } \theta = 1- \cos \theta \ $ |
| Definition of versed cosine (versine) | $ \text{vercosine } \theta = 1+ \cos \theta \ $ |
| please continue | place formula here |
| 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} $ |
| please continue | place formula here |
| Angle sum and differences identities | |
| Angle sum for sine | $ \sin \left( \theta\pm \alpha \right)=\sin \theta \cos \alpha \pm \cos \theta \sin \alpha $ |
| please continue | place formula here |
