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Trigonometric Functions of an Acute Angle
•
Section 1.2
9
are equal and the ratios of the corresponding sides are equal. In fact, we know that com
mon ratio: the sides of
△
ABC
are approximately 2.54 times longer than the corresponding
sides of
△
A
′
B
′
C
′
. So when the American student calculates sin
A
and the German student
calculates sin
A
′
, they get the same answer:
3
△
ABC
∼ △
A
′
B
′
C
′
⇒
BC
B
′
C
′
=
AB
A
′
B
′
⇒
BC
AB
=
B
′
C
′
A
′
B
′
⇒
sin
A
=
sin
A
′
Likewise, the other values of the trigonometric functions of
A
and
A
′
are the same. In fact,
our argument was general enough to work with any similar right triangles. This leads us to
the following conclusion:
When calculating the trigonometric functions of an acute angle
A
, you may
use
any
right triangle which has
A
as one of the angles.
Since we deFned the trigonometric functions in terms of ratios of sides, you can think
of the units of measurement for those sides as canceling out in those ratios. This means
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This note was uploaded on 01/21/2012 for the course MAC 1130 taught by Professor Dr.cheun during the Fall '11 term at FSU.
 Fall '11
 Dr.Cheun
 Calculus, Ratios

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