cosec
Definition
- Noun:
- A trigonometric function: In a right-angled triangle, the cosecant (cosec) of an acute angle is the ratio of the length of the hypotenuse to the length of the side opposite that angle. It is the reciprocal of the sine function.
Usage
- The word cosec is used primarily in mathematics, specifically trigonometry.
- It is typically followed by an angle (e.g., cosec θ, cosec 30°).
- It is often written in its abbreviated form cosec, though the full form cosecant is also common.
Examples
- Noun:
- To find the value of cosec 45°, you first need to know sin 45°.
- The formula is written as cosec θ = hypotenuse / opposite.
- Remember that cosec is undefined for angles where the sine is zero.
Advanced Usage
- In mathematical expressions: Often used in equations and identities, such as cosec² θ = 1 + cot² θ.
- In calculus: The derivative of cosec x is -cosec x cot x.
- Inverse function: The inverse cosecant function is written as arccosec or cosec⁻¹.
Variants and Related Words
- Cosecant (n): The full, unabbreviated form of cosec.
- Csc (n): A common alternative abbreviation for cosecant, especially in American English.
- Reciprocal trigonometric functions: A category including cosec, sec (secant), and cot (cotangent).
Synonyms
- Reciprocal of sine: This is a descriptive synonym, as cosec θ = 1 / sin θ.
Related Phrases
- Cosec of an angle: The standard phrase for its usage.
- Value of cosec: Refers to the numerical result of the cosecant function for a given angle.
Noun
-
ratio of the hypotenuse to the opposite side of a right-angled triangle
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