Physics equations/01-Introduction/A:mathReview

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Common misconceptions[edit]

  and   .


The symbol means . A quick and dirty way to find the percent difference is to divide the big number by the small:


In this right triangle: sin A = a/c; cos A = b/c; tan A = a/b.


Logarithms and exponents are inverse functions[edit]

The implies that the statements are equivalent.

The three most common bases are .

The natural log is defined as .

If and are inverse functions, then:

and , and we write:

and .

Warning: Do not be confused about this notations. The inverses are NOT multiplicative inverses:


Complexities occur when the inverse is not a true function, or equivalently, when the inverse is multi-valued:

Here the problem arises because,


so that knowing the tangent of angle does not precisely tell you what the angle was.

is called the 'arctangent', or the 'inverse tangent'. is called 'arcsine', or the 'inverse sine' and so forth.

Quadratic equation[edit]

This quadratic equation, , has the solutions:


If then


If then