can sin value be 7/5 ?
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Sine
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For other uses, see Sine (disambiguation).
Not to be confused with sign or sign (mathematics).
In mathematics, the sine is a trigonometric function of an angle. The sine of an acute angle is defined in the context of a right triangle: for the specified angle, it is the ratio of the length of the side that is opposite that angle, to the length of the longest side of the triangle (the hypotenuse). For an angle {\displaystyle x}x, the sine function is denoted simply as {\displaystyle \sin x}\sin x.[1][2]
Sine
Sine one period.svg
Basic features
Parity
odd
Domain
(−∞, +∞) a
Codomain
[−1, 1] a
Period
2π
Specific values
At zero
0
Maxima
(2kπ +
π
/
2
, 1)b
Minima
(2kπ −
π
/
2
, −1)
Specific features
Root
kπ
Critical point
kπ +
π
/
2
Inflection point
kπ
Fixed point
0
a For real numbers.
b Variable k is an integer.
More generally, the definition of sine (and other trigonometric functions) can be extended to any real value in terms of the length of a certain line segment in a unit circle. More modern definitions express the sine as an infinite series, or as the solution of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers.
The sine function is commonly used to model periodic phenomena such as sound and light waves, the position and velocity of harmonic oscillators, sunlight intensity and day length, and average temperature variations throughout the year.
The function sine can be traced to the jyā and koṭi-jyā functions used in Gupta period Indian astronomy (Aryabhatiya, Surya Siddhanta), via translation from Sanskrit to Arabic, and then from Arabic to Latin.[3] The word "sine" (Latin "sinus") comes from a Latin mistranslation by Robert of Chester of the Arabic jiba, which is a transliteration of the Sanskrit word for half the chord, jya-ardha.[4]
Right-angled triangle definition
Unit circle definition
Identities
Properties relating to the quadrants
Series definition
Fixed point
Arc length
Law of sines
Special values
Relationship to complex numbers
History
Software implementations
See also
Citations
References
External links
Last edited 6 days ago by Monkbot
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