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| Trigonometry |
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Basic relationships
between trigonometric functions of the same angle |
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Basic
relationships between trigonometric functions of the same angle
shown in the unit circle |
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Basic relationships
between trigonometric functions of the same angle shown in the
tabular form |
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Basic relationships
between trigonometric functions of the same angle, examples |
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Basic relationships
between trigonometric functions of the same angle shown in the
unit circle
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Given relations between the trigonometric functions of the same angle, expressed by absolute value,
are included in the definitions of the functions in right triangles shown in
Fig. a - d, and included in the table below.
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Basic relationships
between trigonometric functions shown in the tabular form
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Basic relationships
between trigonometric functions of the same angle, examples
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| Example:
Find values of other trigonometric functions of
an angle a,
if given sin a
= -
4/5 and
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270° < a
< 360°.
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Solution:
Since a
is a forth-quadrant angle, then
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| Example:
Find the value
of |
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Solution:
Dividing the numerator and
the denominator by
cos2 x,
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| Example:
Prove the
identity |
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| Solution: |
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| Example:
Given
sin x + cos x
= a, find
sin4
x
+ cos4
x
.
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Solution:
Since sin2
x
+ cos2 x = 1 then,
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(sin2
x
+ cos2 x)2 = sin4
x
+ cos4 + 2sin2
x · cos2 x
= 1 or
sin4
x
+ cos4 = 1
-
2sin2
xcos2 x.
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As given sin
x + cos x = a then,
(sin x + cos x)2 =
a2
or sin2
x
+ cos2 x
+ 2sin
x cos x = a2
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therefore, sin
x
· cos x =
(a2
-
1)/2 and
it follows that sin4
x
+ cos4 = 1
- (a2
-
1)2/2.
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| Trigonometry
contents A |
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| Copyright
© 2004 - 2020, Nabla Ltd. All rights reserved. |
