Cosine
Pronunciation
- UK IPA: /ˈkəʊ.saɪn/
- US IPA: /ˈkoʊ.saɪn/
- Homophones: cosign
Full definition of cosine
Noun
cosine
(plural cosines)- (trigonometry) In a right triangle, the ratio of the length of the side adjacent to an acute angle to the length of the hypotenuse. Symbol: cosThese definitions are equivalent to the one above and so do not define different senses of the word.
- (mathematics) The x coordinate of the point on the unit circle at the given anticlockwise angle from the x axis.
- (mathematics) The sum of the real or complex power series
Usage notes
In various branches of mathematics, the cosine of an angle is determined in various ways, including the following:
The x-coordinate of the point on the unit circle at the given anticlockwise angle from the x-axis.
The sum of the real or complex power series
\sum_{n=0}^\infty \frac{(-1)^n x^{2n}{(2n)!} = 1 - {x^2 \over 2} + {x^4 \over 24} - {x^6 \over 720} + {x^8 \over 40320} - \cdots
where x is in radians.