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| align="right" style="padding-right: 1em;" |Definition of tangent | | align="right" style="padding-right: 1em;" |Definition of tangent | ||
| − | |<math> \tan \theta = \frac{\sin \theta}{\cos\theta} </math> [[User: | + | |<math> \tan \theta = \frac{\sin \theta}{\cos\theta} </math> [[User:mboutinformulas|credit]] |
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| align="right" style="padding-right: 1em;" | Definition of cotangent | | align="right" style="padding-right: 1em;" | Definition of cotangent | ||
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| <math>\csc^2 \theta = 1+\cot^2 \theta \ </math> | | <math>\csc^2 \theta = 1+\cot^2 \theta \ </math> | ||
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| − | | align="right" style="padding-right: 1em;" | | + | | align="right" style="padding-right: 1em;" | please continue |
| place formula here | | place formula here | ||
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| align="right" style="padding-right: 1em;" |Half-angle for sine | | align="right" style="padding-right: 1em;" |Half-angle for sine | ||
|<math> \sin \frac{\theta}{2} = \pm \sqrt{ \frac{1-\cos \theta}{2} } \ </math> | |<math> \sin \frac{\theta}{2} = \pm \sqrt{ \frac{1-\cos \theta}{2} } \ </math> | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" |Half-angle for cosine | ||
| + | |<math> \sin \frac{\theta}{2} = \pm \sqrt{ \frac{1+\cos \theta}{2} } \ </math> | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" | please continue | ||
| + | | place formula here | ||
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! style="background: rgb(238, 238, 238) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;" colspan="2" | Angle sum and differences identities | ! style="background: rgb(238, 238, 238) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;" colspan="2" | Angle sum and differences identities | ||
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| align="right" style="padding-right: 1em;" |Angle sum for sine | | align="right" style="padding-right: 1em;" |Angle sum for sine | ||
|<math> \sin \left( \theta\pm \alpha \right)=\sin \theta \cos \alpha \pm \cos \theta \sin \alpha</math> | |<math> \sin \left( \theta\pm \alpha \right)=\sin \theta \cos \alpha \pm \cos \theta \sin \alpha</math> | ||
| + | |- | ||
| + | | align="right" style="padding-right: 1em;" | please continue | ||
| + | | place formula here | ||
|} | |} | ||
Revision as of 08:22, 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 | $ \sin \frac{\theta}{2} = \pm \sqrt{ \frac{1+\cos \theta}{2} } \ $ |
| 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 |
