on April 25, 2022

What is the domain of inverse secant?

Space and Astronomy

Graphs of Inverse Trigonometric Functions

Function Domain Range
tan−1(x) (−∞,∞) (−π2,π2)
cot−1(x) (−∞,∞) (0,π)
sec−1(x) (−∞,−1]∪[1,∞) [0,π2)∪(π2,π]
csc−1(x) (−∞,−1]∪[1,∞) [−π2,0)∪(0,π2]

What is the domain of inverse cosecant?

Lastly, we define the arccosecant function, denoted by arccsc x or csc−1x to be the inverse of the cosecant function with a restricted domain of [−π/2,0)∪(0,π/2], as shown below in red.

What is the domain of inverse trig?

The domain of any inverse trig function ( arcsin , arccos , arctan ) is equal to the range of the corresponding trig function ( sin , cos , tan ).

What is the domain of Secx?

sec x will not be defined at the points where cos x is 0. Hence, the domain of sec x will be R-(2n+1)π/2, where n∈I. The range of sec x will be R- (-1,1).

What is the range of the inverse of secant?

Range of sec⁻¹(x)



As explained above, sec x is positive in the first quadrant (only first quadrant to be considered) and negative in the second quadrant of the common interval [-π/2, π]. We may consider [0, π] as range of y = sec–1(x). sec (π/2) = 1 / cos (π/2) = 1/0 = Undefined.

How do you find the domain of a secant function?

The graph of the cosecant function looks like this: The domain of the function y=csc(x)=1sin(x) is all real numbers except the values where sin(x) is equal to 0 , that is, the values πn for all integers n . The range of the function is y≤−1 or y≥1 .

Is there inverse Cosecant?

Definition: The inverse cosecant function denoted by ” ” is defined to be the inverse of the domain-restricted cosecant function. The restricted-domain tangent, secant, cotangent, and cosecant functions and their inverses are graphed below in that order.

What quadrants are inverse secant in?

The inverse cos, sec, and cot functions return values in the I and II Quadrants (between 0 and 2\pi ), and the inverse sin, csc, and tan functions return values in the I and IV Quadrants (between -\frac{\pi }{2} and \frac{\pi }{2}), with negative values in Quadrant IV).

Is secant the inverse of cosine?

Secant is the reciprocal of cosine. Cotangent is the reciprocal of tangent. When solving right triangles the three main identities are traditionally used.

What is the cosecant inverse of 2?

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.

How do you use arccsc?

Video quote: And that tells me the answer is 41.8 degrees another way you can do this would be to do the following. Would simply go to do 3 divided by 2 enter.

How do you find the inverse secant of 2?

Video quote: And the reciprocal of 2 over 1 is 1/2. And therefore inverse secant of 2 is equal to inverse cosine of 1/2.



How do you find arcsec without a calculator?

Video quote: Must be in the open interval from 0 degrees to 180 degrees or in radians theta. Must be on the open interval from 0 to pi radians. And again this equation means that secant theta.

How do you find arcsec of 2?

The exact value of arcsec(2) is π3 .

What does arcsec mean?

Definitions of arcsec. the inverse function of the secant; the angle that has a secant equal to a given number. synonyms: arc secant, arcsecant, inverse secant. type of: circular function, trigonometric function.

Is arcsec the same as cos?

The functions are usually abbreviated: arcsine (arcsin), arccosine (arccos), arctangent (arctan) arccosecant (arccsc), arcsecant (arcsec), and arccotangent (arccot).



Math2.org Math Tables:

sin(q) = opp/hyp csc(q) = 1/sin(q)
cos(q) = adj/hyp sec(q) = 1/cos(q)
tan(q) = sin(q)/cos(q) cot(q) = 1/tan(q)