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what is sec the inverse of

by Prof. Erik Bogan Published 3 years ago Updated 2 years ago

The secant is the reciprocal of the cosine. It is the ratio of the hypotenuse to the side adjacent to a given angle in a right triangle.

What is sec inverse equal to?

arcsecThe inverse of sec is arcsec. In trigonometry, the inverse of the secant function is the arcsec.

Is sec the inverse of tan?

The functions are usually abbreviated: sine (sin), cosine (cos), tangent (tan) cosecant (csc), secant (sec), and cotangent (cot)....Math2.org Math Tables:sin(q) = opp/hypcsc(q) = 1/sin(q)cos(q) = adj/hypsec(q) = 1/cos(q)tan(q) = sin(q)/cos(q)cot(q) = 1/tan(q)

Is sec inverse of sin?

Cosecant theta is 1 over y and y is sine theta. So cosecant theta is the reciprocal of sine.

What is the sec inverse of 1?

1 Answer. sec−11=0 .

Is Cos 1 the same as sec?

cos x−1, sometimes interpreted as (cos(x))−1 = 1cos(x) = sec(x) or secant of x, the multiplicative inverse (or reciprocal) of the trigonometric function cosine (see above for ambiguity)

What is the inverse of sin?

Arcsine is the inverse of sine function. It is used to evaluate the angle whose sine value is equal to the ratio of its opposite side and hypotenuse. Therefore, if we know the length of opposite side and hypotenuse, then we can find the measure of angle.

Is sec inverse trig?

For every trigonometry function such as sec, there is an inverse function that works in reverse. These inverse functions have the same name but with 'arc' in front. So the inverse of sec is arcsec etc. When we see "arcsec A", we interpret it as "the angle whose secant is A".

What does sec mean in math?

Secantmore ... In a right angled triangle, the secant of an angle is: The length of the hypotenuse divided by the length of the adjacent side. The abbreviation is sec.

What is sec formula?

Secant is one of the ratios that is derived from the cosine ratio. The secant formula helps in finding out the hypotenuse, the length, and the adjacent side of a right-angled triangle. The formula is sec ⁡θ = H/B.

What is the secant inverse of 2?

5:366:43Evaluate Inverse Secant Expressions Using the Unit Circle (Nice Values)YouTubeStart of suggested clipEnd of suggested clipFunction value is the reciprocal. And the reciprocal of two over one is one half and thereforeMoreFunction value is the reciprocal. And the reciprocal of two over one is one half and therefore inverse secant of two is equal to inverse cosine of one.

What is the secant inverse of 0?

The exact value of sec(0) is 1 . Interchange the variables. Since y cannot be isolated, an inverse cannot be found.

How do you do inverse secant on a calculator?

0:091:22Inverse Reciprocal Trig on TI 84 Graphing Calculator - YouTubeYouTubeStart of suggested clipEnd of suggested clipWe press second and sign for the inverse sine or arc sine. And then 1/2. No need to closeMoreWe press second and sign for the inverse sine or arc sine. And then 1/2. No need to close parenthesis just press Enter.

What is Sec Inverse x?

Sec Inverse x is the inverse trigonometric function of the secant function. Mathematically, it is denoted by sec -1 x. It can also be written as arcsec x. In a right-angled triangle, the secant function is given by the ratio of the hypotenuse and the base, that is, sec θ = Hypotenuse/Base = x (say).

Domain and Range of Sec Inverse x

We know that sec inverse x is an inverse function of the secant function. Also, it is necessary for a function to be bijective (one-one and onto) to have an inverse. Hence, to make the secant function bijective, we take the principal value branch as the range of sec inverse x.

Sec Inverse x Graph

Now, let us understand more about sec inverse x and check its domain and range using the graph of arcsec. We can plot the graph of sec inverse x using some of its points. By plotting the below-given points on a graph with the angle on Y-axis and real numbers on X-axis given by y = sec -1 x:

Sec Inverse x Derivative and Integration

Now, we will determine the derivative of sec inverse x and the integral of sec inverse x. To determine the derivative of arcsec, we will use implicit differentiation. Assume y = sec -1 x ⇒ sec y = x. We need to determine the value of dy/dx. Now, differentiate sec y = x with respect to x. We have,

Sec Inverse x Formulas

Now, that we have explored the concept of sec inverse x, let us now see some formulas of sec inverse x that are used to solve various mathematical trigonometric problems:

FAQs on Sec Inverse x

Sec Inverse x is the inverse trigonometric function of the secant function. Mathematically, it is denoted by sec -1 x or arcsec x or sec -1 (Hypotenuse/Base) [in the context of a right-angled triangle].

What are Inverse Trigonometric Functions?

Inverse trigonometric functions are also called “ Arc Functions ” since, for a given value of trigonometric functions, they produce the length of arc needed to obtain that particular value.

Inverse Trigonometric Functions Graphs

There are particularly six inverse trig functions for each trigonometry ratio. The inverse of six important trigonometric functions are:

Inverse Trigonometric Functions Table

Let us rewrite here all the inverse trigonometric functions with their notation, definition, domain and range.

Inverse Trigonometric Functions Derivatives

The derivatives of inverse trigonometric functions are first-order derivatives. Let us check here the derivatives of all the six inverse functions.

Inverse Trigonometric Functions Properties

The inverse trigonometric functions are also known as Arc functions. Inverse Trigonometric Functions are defined in a certain interval (under restricted domains). Read More on Inverse Trigonometric Properties here.

The inverse secant function - arcsec

For every trigonometry function such as sec, there is an inverse function that works in reverse. These inverse functions have the same name but with 'arc' in front. So the inverse of sec is arcsec etc. When we see "arcsec A", we interpret it as "the angle whose secant is A".

Large and negative angles

In a right triangle, the two variable angles are always less than 90° (See Interior angles of a triangle ). But we can in fact find the secant of any angle, no matter how large, and also the secant of negative angles. For more on this see Functions of large and negative angles .

Graph of the secant function

Because the secant function is the reciprocal of the cosine function, it goes to infinity whenever the cosine function is zero.

The derivative of sec (x)

In calculus, the derivative of sec (x) is sec (x)tan (x). This means that at any value of x, the rate of change or slope of sec (x) is sec (x)tan (x) .

Using the Arcsecant Calculator

To use the tool to find the angle from a known secant, enter the ratio and the units you'd like and compute.

What is the arcsecant or inverse secant?

Arcsecant is the inverse of the secant, which is the ratio of the hypotenuse, or longest side, to the adjacent side in a right triangle.

Arcsecant as a formula

Inverse secant is usually abbreviated as "arcsec" or "asec", as in the following equation:

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