Warmup S implify the following fractions without a calculator leaving all fractions improper Why are there 360 degrees in a circle What are radians Figure out the circumference of the circle ID: 378813
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Slide1
3.2 RadiansSlide2
Warm-up:
S
implify the following fractions without a calculator, leaving all fractions improper.Slide3
Why are there 360 degrees in a circle?Slide4
What are radians?
Figure out the circumference of the circle.
Figure out how big the fraction of the circumference we’re dealing with (arc length).Figure out how many times the radius of the circle fits into that arc.
That value is the measure of your angle in radians. Slide5
Radian Visual AidSlide6Slide7
Radian Investigation – do we notice anything about theta vs. r (radius)?Slide8
In summary, radians DO NOT depend on the radius at all (why??) and have very little to do with circles. Slide9
You are probably asking yourself “Self, why do we need another way to measure angles if we already have degrees?”
A: Because the calculus of trig functions does not work out nicely in degrees but works out brilliantly in radians. You are learning how to work with radians now so that you can work at all in the future.Slide10
What is bigger 1 degree or 1 radian?Slide11
How to convert angles to radiansSlide12Slide13
Convert from R to D or D to R
If the number has a degree symbol (
o) then it is an angle measure in degrees.
If the number does not have the degree symbol, it is an angle measure in radians.
That is a rule for ALWAYS, not just these problems. Slide14
TIP
Here is how I remember to either multiply by
π
/180 or 180/
π
:
Angle measures in radians
are often (but not always) in
terms of
π
(ex: Theta = 3
π
or
π
/4). So to convert the angle to degrees you would multiply it by 180/
π
to divide out
π
.
Angle measures in degrees are almost NEVER in terms of
π
(ex: Theta = 360
o
). To convert to radians, for every 180 you divide out you want to multiply the angle by
π
, so multiply by
π
/180.Slide15Slide16