Radians and Degrees
•
Section 4.1
89
One reason why radians are used is that the scale is smaller than for degrees. One revolu
tion in radians is 2
π
≈
6
.
283185307, which is much smaller than 360, the number of degrees
in one revolution. The smaller scale makes the graphs of trigonometric functions (which we
will discuss in Chapter 5) have similar scales for the horizontal and vertical axes. Another
reason is that often in physical applications the variables being used are in terms of arc
length, which makes radians a natural choice.
The default mode in most scientific calculators is to use degrees for entering angles. On
many calculators there is a button labeled
✄
✂
a0
✁
DRG
for switching between degree mode (D),
radian mode (R), and
gradian
mode (G).
1
On some graphing calculators, such as the the TI
83, there is a
✄
✂
a0
✁
MODE
button for changing between degrees and radians. Make sure that your
calculator is in the correct angle mode
before
entering angles, or your answers will likely be
way off. For example,
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 Fall '11
 Dr.Cheun
 Calculus, Trigonometry, radian mode

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