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| Applications
of Trigonometry |
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Applications
of Trigonometry in Physics |
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Applications in physics |
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An example of using trigonometry in
optics |
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Applications of trigonometry in physics
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Physical laws, as results and available experimental data we explain and write applying mathematics methods. We can show that trigonometry is often used in these
methods.
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Take for example construction shown in
the below figure that is loaded by a force FG.
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Determine the forces which act in the cable a
and b
that make the angle a
and b
with horizontal, respectively.
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to its components Fa
and Fb
by using the parallelogram method on the vector diagram, thus in
DABC |
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An example of using trigonometry in
optics
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Two parallel light rays enter at an angle
a
to the normal of the surface of a triangular glass prism and pass through the prism. The paths of the rays (red) are shown in diagram
below, taking into account the index of refraction for glass
n = 1.5.
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a) At what angle (denoted as
g) upper ray exits the prism?
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b) Find the declination d
of the lower ray while exits the prism expressed in terms of the height
h
of the incidence and the side
a
of the prism.
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| Solution: Index
of refraction
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a) g
= a
-
b
+ a1
-
b1,
b
+ b1 =
60° => b1 =
60° -
b,
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g
= a
-
b
+ a1
-
60° + b =
a
+ a1
-
60° = a1
-
30°,
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Note that triangles, AEC and
EBD
are similar as their corresponding
angles are equal.
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| Geometry
and use of trigonometry contents - B |
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