Posted by Brad Paul on October 19, 2002 at 16:22:25:
In Reply to: one more question... posted by Barry on October 19, 2002 at 15:51:30:
: Thanks Mr P.
: One last question:
: : [t (radians) such that 0 < t < (1/2)(pi) ]
: : T(t) = (5 / x)[t + 2(cos t)]
: It is stated that "t" is in radians.
: Then, what does "cos t" mean here?
: I thought you could only have stuff like cos(30 degrees).
: Is it significant that they have cos t, not cos(t)?
It is good your are concerned with the details of notation.
Both cos t and cos(t) are the something but the first is not a good
way or writing it. For example what does this mean?
cos 2x+pi/2 is it cos(2x)+pi/2 or cos(2x+pi/2)
It is best to always use a pair or () after a function like:
log(2x+r) or sin(2 pi t) etc.
If I wrote cos t earlier I was sloppy and should be more careful.
As far as the t in cos(t) or sin(t) it is a measure of an angle. The
best way to measure an angle is in radians. You have to use radians
when using the series representation of trig functions. The only reason
we also divide a circle up into 360 degrees is because the ancient
Babylonians liked how many ways the number 360 can be evenly divided.
There are lots of "taken for granted" things that are rather arbitrary.
We have 12 months because there are about 12 full moons in a year.
We count with a base 10 number system because we have ten fingers.
A mile was 1000 paces of a roman legion until it was stretched to match
up with a furlong.
etc...