Trigonometry

[Brian White]

Anyone know of a good web site or book that derives from the most basic
first principles all of the relations between sin(theta) cos(theta)
tan(theta) and how they are derived in relation to circles? I'm not just
talking about how sin(theta) is opposite over adjacent, but WHY it is so.
For instance, what calcualtion does the calculator do when you enter radians
and then hit th sin or cosine button. How does it come up with the answer.
Brian White

[slacker]

im not sure, but someone told me that calculators use a taylor series
expansion of sin/cos to approximate the values.

Post by Brian White
Anyone know of a good web site or book that derives from the most basic
first principles all of the relations between sin(theta) cos(theta)
tan(theta) and how they are derived in relation to circles? I'm not just
talking about how sin(theta) is opposite over adjacent, but WHY it is so.
For instance, what calcualtion does the calculator do when you enter radians
and then hit th sin or cosine button. How does it come up with the answer.
Brian White

[operator jay]

Post by slacker
im not sure, but someone told me that calculators use a taylor series
expansion of sin/cos to approximate the values.

I have heard the same. A calculator will also take the angle and reduce it
so that the series si calculated on a value between 0 and 45 degrees or 0and
22.5 degrees or something, using trgi tricks.

Post by slacker

Post by Brian White
Anyone know of a good web site or book that derives from the most basic
first principles all of the relations between sin(theta) cos(theta)
tan(theta) and how they are derived in relation to circles? I'm not just
talking about how sin(theta) is opposite over adjacent, but WHY it is so.
For instance, what calcualtion does the calculator do when you enter radians
and then hit th sin or cosine button. How does it come up with the answer.
Brian White

I probably have some text books but I doubt that'd help you. Are you
familiar with complex exponentials and
e ^ (j theta) = cos theta + j sin theta ?
I think that can help with a lot of the algebra in working with trig IDs and
the like. I believe that relationship is called Euhler's Identity
(pronounced "oiler"). You'll want to look it up online someplace to make
sure I didn't blow a j or a - or anything stupid.