The lecture notes for the graphs of tangent
and cotangent are in the links below
Lecture Notes f(x) = tan(x)
Lecture Notes f(x) = cot(x)
Radian Measure If you think about it why are there 360º in a single revolution? It is somewhat
arbitrarywhy not 100º ? Actually its based on the number of days in a year. In Calculus and applied mathematics a different measure is used which relates angle
to distance and hence can be related to time. After all the true power of trig is modeling periodic motion where we talk about
sin(t) or cos(t) where t is time. Radian measure
comes from the arclength formula s = r θ. In particular if we are on a circle of radius 1 (the unit circle) then we
have simply s = θ. The radian measure is equal
to the distance traveled on the unit circle starting at the pt
(1,0) traveling counter clockwise. Therefore there are 2π radians in one revolution. See Animation 1 below.
Radian Measure
As with the convention with degrees a clockwise
rotation is considered negative. In this case the
radian measure is the negative of the distance traveled clockwise around the unit circle.
Negative Radian Measure
One of the advantage of radian measure is that
it is a unitless real number. From s = r Θ
since s and r are distances whatever unit is being used cancels from both sides and so Θ is just a number
without units.
The Smart BunnyA very short story by Kurt Vonnegut Jr.
©20082010
Kelly Liakos

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