What is the reciprocal of sine called?
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What is the reciprocal of sine called?
cosecant
The cosecant is the reciprocal of the sine. The secant is the reciprocal of the cosine. The cotangent is the reciprocal of the tangent.
What is the relationship between sine and cosecant?
tan x = sin x cos x . The cotangent of x is defined to be the cosine of x divided by the sine of x: cot x = cos x sin x . The secant of x is 1 divided by the cosine of x: sec x = 1 cos x , and the cosecant of x is defined to be 1 divided by the sine of x: csc x = 1 sin x .
Are csc and sin reciprocals?
Cosecant is the reciprocal of sine. Its abbreviation is csc. To determine csc, just flip sin over. Secant is the reciprocal of cosine.
What is cosecant of theta?
The reciprocal sine function is cosecant, csc(theta)=1/sin(theta).
Why is it called cosecant?
The origin of secant can be traced to latin as well. It comes from the latin word secare, meaning “to cut”. Note that if this secant line is extended, it cuts the unit circle neatly in half. Again, the cosecant can be thought of as being the same as the same function with respect to the y-axis.
What is the reciprocal of cosecant?
The cosecant is the reciprocal of the sine. The secant is the reciprocal of the cosine. The cotangent is the reciprocal of the tangent.
What is the inverse of cosecant?
The inverse function of cosecant. Basic idea: In order to find csc-1 2, we ask “what angle has cosecant equal to 2?” The answer is 30°. As a result we say csc-1 2 = 30°. In radians this is csc-1 2 = π/6….
| csc-1 | cosec-1 |
|---|---|
| Csc-1 | Cosec-1 |
| arccsc | arccosec |
| Arccsc | Arccosec |
How do you find cosecant on the unit circle?
The cosecant function is the reciprocal of the sine function (cscx=1sinx) x = 1 sin . It can be found for an angle t by using the y -coordinate of the associated point on the unit circle: csct=1y t = 1 y . The cotangent function is the reciprocal of the tangent function (cotx=1tanx=costsint) x = 1 tan .
What is the cosecant function?
The cosecant function is the reciprocal of the sine function. The sine function is the opposite side divided by the hypotenuse, so the cosecant function is the hypotenuse divided by the opposite side. These functions give a relationship or ratio between the sides based on the given angles.
What is the definition of the cosecant?
Definition of cosecant 1 : a trigonometric function that for an acute angle is the ratio between the hypotenuse of a right triangle of which the angle is considered part and the leg opposite the angle.
Why is the sine function called sine?
The word sine originally came from the latin sinus, meaning “bay” or “inlet”. When the term was translated to latin in the twelfth century, jb was incorrectly read as jaib (meaning “bay” or “inlet”), and thus translated as sinus. The sine function has a direct connection to chords on a circle.