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Calculus/Trig - Unit Circle

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Expert: - 2/16/2009


Question
I hope that my question actually makes sense. I am in the 11th grade and we are studying trigonometry. The Unit Circle is one thing that just doesn't click with my algebra-oriented brain. I guess my question is, how are the radians and things determined? Also, how do you find the arc length with circles. I hope my questions aren't too broad. Thanks for your time. -Allison

Answer
It is known that a circle is 360°.
It is also known that a circle is 2π radians.
This means that to convert from degrees to radians,
mutliply by π/180°.

Note that the disance around a cirle is 2πr.

Since there are 2π radians in a circle, that means the
distance around a section of circle (the arc length )
with angle Θ is Θr when Θ is in radians.  That's one
of the reasons thatradians were chose to be the size
they are.

So to convert from radians back to degrees,
can you guess what to do?



That's right!  Multiply by 180°/π.

What is known is that 90° is a right angle.
Another key concept that will arise is that
a right angle is π/2 radians.

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