Difference between revisions of "User:Temperal/The Problem Solver's Resource1"
(→Basic Facts: rmv redundancy) |
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===Terminology and Notation=== | ===Terminology and Notation=== | ||
− | <math>\cot A=\frac{1}{\tan A}</math>, but <math>\cot A\ne\tan^{-1} A}</math>. | + | <math>\cot A=\frac{1}{\tan A}</math>, but <math>\cot A\ne\tan^{-1} A}</math>, the former being the reciprocal and the latter the inverse. |
<math>\csc A=\frac{1}{\sin A}</math>, but <math>\csc A\ne\sin^{-1} A}</math>. | <math>\csc A=\frac{1}{\sin A}</math>, but <math>\csc A\ne\sin^{-1} A}</math>. | ||
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<math>\sec A=\frac{1}{\sin A}</math>, but <math>\sec A\ne\cos^{-1} A}</math>. | <math>\sec A=\frac{1}{\sin A}</math>, but <math>\sec A\ne\cos^{-1} A}</math>. | ||
− | + | Speaking of inverses: | |
<math>\tan^{-1} A=\text{atan } A=\arctan A</math> | <math>\tan^{-1} A=\text{atan } A=\arctan A</math> |
Revision as of 18:27, 10 January 2009
Introduction | Other Tips and Tricks | Methods of Proof | You are currently viewing page 1. |
Trigonometric Formulas
Note that all measurements are in radians.
Basic Facts
The above can all be seen clearly by examining the graphs or plotting on a unit circle - the reader can figure that out themselves.
Terminology and Notation
, but $\cot A\ne\tan^{-1} A}$ (Error compiling LaTeX. Unknown error_msg), the former being the reciprocal and the latter the inverse.
, but $\csc A\ne\sin^{-1} A}$ (Error compiling LaTeX. Unknown error_msg).
, but $\sec A\ne\cos^{-1} A}$ (Error compiling LaTeX. Unknown error_msg).
Speaking of inverses:
Sum of Angle Formulas
or or
Pythagorean identities
for all .
Other Formulas
Law of Cosines
In a triangle with sides , , and opposite angles , , and , respectively,
and:
Law of Sines
Law of Tangents
For any and such that ,
Area of a Triangle
The area of a triangle can be found by