cosine
/'kousain/
Definition
- Noun:
- A trigonometric function: In a right-angled triangle, the cosine of an acute angle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.
- A mathematical value: The cosine is a fundamental function in trigonometry, often abbreviated as "cos".
Usage
- The cosine is used to solve problems involving right triangles, waves, oscillations, and circular motion.
- It is a periodic function with values ranging from -1 to 1.
- In mathematics and physics, it is commonly used alongside the sine and tangent functions.
Examples
- Noun:
- The cosine of 60 degrees is 0.5.
- In the equation, you need to calculate the cosine of the angle theta.
- The graph of the cosine function is a wave that starts at its maximum value.
Advanced Usage
"Law of Cosines": A theorem relating the lengths of the sides of any triangle to the cosine of one of its angles. It generalizes the Pythagorean theorem.
- We used the law of cosines to find the length of the unknown side.
"Cosine similarity": In data science and text analysis, a measure of similarity between two vectors, calculated as the cosine of the angle between them.
- Cosine similarity is often used to compare documents in natural language processing.
Variants and Related Words
Cos (abbr.): The standard abbreviation for cosine.
- Cos(π) equals -1.
Arccosine / Inverse cosine (n): The inverse function of the cosine, which returns an angle given a cosine value.
- The arccosine of 0.5 is 60 degrees.
Hyperbolic cosine (cosh) (n): A related function used in hyperbolic geometry and calculus.
Synonyms
- Trigonometric ratio: A more general term for functions like sine, cosine, and tangent.
Related Phrases
- "Cos squared": Refers to the square of the cosine value, written as cos²(θ).
- A fundamental identity is that sin²(θ) + cos²(θ) = 1.
Noun
-
ratio of the adjacent side to the hypotenuse of a right-angled triangle
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