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| Trigonometry |
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Calculation of values of trigonometric functions
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Calculation of
values of trigonometric functions of an arbitrary angle x, examples |
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Calculation of values of trigonometric functions of an arbitrary angle
x examples
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| Example:
Calculate sin
1110°.
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Solution: To use the expression x =
a +
k · 360° we should divide given angle by
360°
to get an integer multiple
k and remaining angle
a,
thus
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| Example:
Calculate cos
(-
77p/4).
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Solution:
Since cos
(-
x) = cos x
we can write cos
(-
77p/4)
= cos 77p/4,
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then, divide given x
by
2p,
x = 77p/4
= 19p
+ p/4
= 9 · 2p
+ 5p/4
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so that, cos
(-
77p/4)
= cos 77p/4
= cos (9 · 2p
+ 5p/4)
= cos 5p/4.
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As the terminal side of the angle 5p/4
lies in the third quadrant we use cos
(p
+ a) = -
cos a
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therefore, cos
5p/4
= cos
(p
+ p/4) =
-
cos p/4
= -
Ö2/2.
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| Example:
Calculate tan
817° 35′ 42″.
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Solution:
According to x =
a +
k · 180°
we divide the given angle x
by 180° to
determine k
and a,
so
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x = 817° 35′ 42″ = 97° 35′ 42″ + 4 · 180°
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thus, tan
817° 35′ 42″ = tan (97° 35′ 42″ + 4 · 180°) = tan 97° 35′ 42″,
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as it is second-quadrant angle we use tan
(180° -
a) = -
tan
a
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that is, 180° -
a =
179° 59′ 60″ -
97° 35′ 42″ = 82° 24′ 18″
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therefore, tan
97° 35′ 42″ = tan (180° -
82° 24′ 18″) = -
tan 82° 24′ 18″ =
-
7.49964.
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When we use a scientific calculator to find values for trigonometric functions, a given angle should be entered as decimal degree in DEG mode, so input
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82.2418
INV ®DEG
=> 82.405° TAN
=>
7.49964367.
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| Example:
Calculate cot
27p/7.
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Solution:
Decompose the angle to
x =
a +
k · p, that is, x =
27p/7 =
(3 + 6/7)p =
6p/7
+ 3p
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thus, cot
27p/7 =
cot (6p/7
+ 3p) =
cot 6p/7
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since for a fourth-quadrant angle
holds cot
(2p
-
a) = -
cot
a
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then, cot
6p/7 =
cot (2p
-
p/7)
= -
cot
p/7 =
-
2.07652.
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When we use calculator we set it in
the RAD mode using DRG key, then enter,
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INV p
¸
7 =
0.44879895 TAN
(0.481574618) 1 / x
=>
2.076521397.
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That is, the value of the function cotangent we calculate as the reciprocal value of the function
tangent, as
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cot x = 1/tan x.
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| Trigonometry
contents A |
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| Copyright
© 2004 - 2020, Nabla Ltd. All rights reserved. |
