Meaning & use
cosec
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Meaning
nouncountablemathematics
A shortened name for cosecant, the trigonometric ratio found by dividing one by the sine of an angle.
Grammar: Usually used with an angle: cosec of 30 degrees; also written cosec x.
Patterns
- cosec of something
- cosec x
Since sin 30 degrees is one half, cosec 30 degrees equals two.
Write cosec x as one over sin x before you simplify the equation.
In the exam, she mistook cosec for sec and lost a mark.
Word forms
| plural | cosecs |
|---|
Common combinations
- cosec of an angle
- Find the cosec of an angle of 90 degrees.
- cosec x
- Differentiate cosec x with respect to x.
- cosec squared
- The identity links cosec squared to cotangent squared.
- reciprocal of sine
- Cosec is the reciprocal of sine, so it is never below one in size.
Synonyms and how they differ
- cosecant
- Cosecant is the full form of the term, used in textbooks, while cosec is the shorthand used in formulas and calculations.
- csc
- Csc is the usual American abbreviation, while cosec is more common in British and international books.
Word family
Commonly confused: cosec or cos? cosec or sec?
cosec vs cos
Cos is short for cosine, a different function, while cosec is the reciprocal of sine and starts with the same letters.
cosec vs sec
Sec is the reciprocal of cosine, not of sine, so it should not be swapped with cosec.
Practice
If sin θ = 0.25, what is cosec θ?
Choose one answer.
Cosec θ is 1 divided by sin θ, so 1 ÷ 0.25 = 4. The value 0.25 is the sine itself, so it is a tempting but wrong choice.
Make it your own
Write a sentence using “cosec”, then check it and compare it with the examples above.