Expert: Abe Mantell - 1/17/2005

Question
Basic questions:  What is the purpose of trigonometic functions in Calculus?

What is the purpose of the secant, cosecant and tangent ratios?

How are they used in practical mathematics?

What is the purpose of the natural logarithm in calculus?

What are some of the practical applications of natural logarithms besides future financial value calculations?

Thanks so much!

Bill Ferris  

Answer
Trig functions are useful to describe phenomena that
is periodic...such as problems involving rotations and life-cycles (for example).

sec, and csc are just convenient functions to
use for the recipricols of cos, and sin.
tan is just a convenient function for the ratio
of sin and cos...

How are they used?  Again, to describe periodic
phenomena...check any precalculus book...

logarithms are the inverse functions of exponential
functions...they are typically used for that purpose.
Again, see any precalculus text.  Some applications
include: (aside from finance)
1. the Richter Scale - used for measuring the strength
of earthquakes...uses a logarithmic scale.
2. pH - used for measuring the strength of acids and
bases in chemistry...uses a logarithmic scale...

You can find quite a bit about all this on the Internet.
Try using google.com

Abe