Is sin inverse X equal to cosec X?
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Is sin inverse X equal to cosec X?
sin^-1(1/x) = cosec^-1(x); cos^-1(1/x) = sec^-1(x); tan^-1(1/x) = cot^-1(x) for x>0 and -pi + cot^-1(x) for x<0.
Is cosec inverse of sin?
The cosecant is the reciprocal of the sine. It is the ratio of the hypotenuse to the side opposite a given angle in a right triangle.
What is the value of cosec inverse X?
We know that the range of the principal value branch of cosec-1(x) is [-π/2, π/2] – {0} and cosec(π/2) = 1. So, the principal value of cosec-1(1) = π/2.
Why is sin 1 not cosec?
Is sine inverse equal to cosec function? Sine inverse or arcsine is the inverse of sine function which returns the value of angle for which sine function is equal to opposite side and hypotenuse ratio. But cosec function is the reciprocal of sine function and is not equal to sine inverse.
What is the domain of the function Cosec inverse?
Domain and Range of Trigonometry Functions
| Domain | Range | |
|---|---|---|
| cos -1 | [–1, 1] | [0,π] |
| tan -1 | R | (-π/2,π/2) |
| cosec -1 | R – (–1, 1) | [-π/2,π/2] – {0} |
| sec -1 | R – (–1, 1) | [0,π]-{π/2} |
What is cosec equal to?
1 cos 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 .
How do you find the value of cosec?
We can use trigonometric identities to represent cosec 0° as, cosec(180° – 0°) = cosec 180° -cosec(180° + 0°) = -cosec 180° sec(90° – 0°) = sec 90°…Using trigonometry formulas, we can represent the cosec 0 degrees as:
- ± 1/√(1-cos²(0°))
- ± √(1 + tan²(0°))/tan 0°
- ± √(1 + cot²(0°))
- ± sec 0°/√(sec²(0°) – 1)
- 1/sin 0°
Is Arcsine inverse sine?
Sal introduces arcsine, which is the inverse function of sine, and discusses its principal range.
Is sin inverse increasing or decreasing?
Arc(sinx) is the inverse function of sinx hence there domain and range are switched. Therefore it is clearly increasing.