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
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:
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.
This quadratic equation, , has the solutions: