What is the principal value of cosec − 1x?

1 Answer. As the principal branch

principal branch

A branch cut, usually along the negative real axis, can limit the imaginary part so it lies between −π and π. These are the chosen principal values. This is the principal branch of the log function. Often it is defined using a capital letter, Log z.

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Principal branch - Wikipedia

of cosec^-1 x is [-π/2, π/2] – {0}.

What is the principal value branch of cosec − 1x?

So, the principal value of cosec^-1(1) = π/2.

What is the principal value of cosec?

Therefore, the principal value of cosec−1(2) is 6π

What is cosec inverse?

Given a triangle rectangle, we define the cosecant, the secant and the cotangent of an angle as the inverse ratios of the sine, the cosine and the tangent, respectively. ⁡ : the cosecant is the inverse of the sine or, also, its multiplicative inverse: ⁡ ( x ) = 1 sin ⁡

What is principal value of inverse trigonometric functions?

Let us recall that the principal value of a inverse trigonometric function at a point x is the value of the inverse function at the point x , which lies in the range of principal branch. For instance, the principal value of cos⁻¹ (√3/2) is π/6. Since π /6 ∈ [0, π].

Principal value of cosec inverse

What is the domain of inverse cosine?

The domain of the inverse cosine function is [−1,1] and the range is [0,π] . That means a positive value will yield a 1st quadrant angle and a negative value will yield a 2nd quadrant angle.

How do you find the domain of an inverse trig function?

To find the domain and range of inverse trigonometric functions, switch the domain and range of the original functions. Each graph of the inverse trigonometric function is a reflection of the graph of the original function about the line y=x .

What is the principal value of cosec inverse minus one by two?

cosec^-1(2) Therefore, principal value of cosec^-1(2) = π/6.

What will be the principal value of cosec inverse minus under root 2?

Therefore, the principal value of cosec−1(−2 ) is −4π.

What is the principal value of cosec (- 1 )(- sqrt 2 ))?

Solution : Let `"cosec"^(-1)(-sqrt(2))=x`, where `xin [-pi/2,pi/2]-{0}`. <br> Then, `"cosec"x=-sqrt(2)=-"cosec"pi/4="cosec"(-pi/4) rArr x=-pi/4`. Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

How do you find the principal value?

The principal value of the trigonometric function can be calculated by first breaking the angle into a sum of a larger angle and the acute angle. Further after finding the value of the acute angle for the trigonometric function, we can find the principal solution of the trigonometric function.

Which of the following is the principal value of branch?

We know that, the principle value branch of cos−1 x is [0,π]

What is the principal value of tan inverse?

Since we know that the range of principal value of tan is (-π / 2, π / 2) and the value of the tangent function is equal to 1 at π/4 radians, therefore the value of tan inverse 1 is equal to π/4 radians.

Is cosecant inverse of sine?

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. It generates the value of angle. But cosec function is the reciprocal of sine function and is not equal to sine inverse.

What is csc equal to?

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 .

Is cosecant and inverse trig function?

We already know that the cosecant function is the reciprocal of the sine function. This will be used to derive the reciprocal of the inverse sine function. Because cosecant and secant are inverses, \begin{align*}\sin^{-1} \frac{1}{x} = \csc^{-1} x\end{align*} is also true.

How do you write cosecant?

Cosecant is one of the main six trigonometric functions and is abbreviated as csc x or cosec x, where x is the angle. In a right-angled triangle, cosecant is equal to the ratio of the hypotenuse and perpendicular. Since it is the reciprocal of sine, we write it as csc x = 1 / sin x.

What is the principal value of cosec inverse minus 2 by root 3?

Therefore, the set of values of cosec−1( 2)=3π

What is principal value in math?

In mathematics, specifically complex analysis, the principal values of a multivalued function are the values along one chosen branch of that function, so that it is single-valued. The simplest case arises in taking the square root of a positive real number.

What is the value of cosec 2?

Cosec 2 degrees is the value of cosecant trigonometric function for an angle equal to 2 degrees. The value of cosec 2° is 28.6537 (approx).