Cos Inverse Formula

Cos Inverse Formula600

Inverse trigonometric functions are used to find the angles of a triangle. To find the angle from the base and hypotenuse, the inverse cos formula is used. The inverse cos function also has some properties related to the domain and range for which the domain is [-1,1]. Cos Inverse Formula is discussed in this article.

What Is Cos Inverse Formula?

What is the Cos Inverse Formula? The Cos Inverse Formula is used to find the angle from the base and hypotenuse. The inverse cos function also has some properties related to domain and range. The Cos Inverse Formula function is also called the “arc function”. 

Cos Inverse Formula is the important inverse trigonometric function. Mathematically, it is written cos-1(x) and is the inverse of the trigonometric cosine cos(x). Note that arc cosine is not the reciprocal of cos x. There are six inverse trigonometric functions sin-1x, cos-1x, tan-1x, csc-1x, sec-1x, and cot-1x.

Arc cos Questions

It is advisable to understand the Cos Inverse Formula with an example. The arc cosine is used to determine angle measurements from the trigonometric ratio cos x values. In this article, one will understand the formula of the arc cosine function, its domain and range, and its graph. One can also determine the derivative and integral of cos inverse x to better understand its properties through this article. The cos inverse x can also be written as arccos x as if y = cos x ⇒ x = cos-1(y). Look at some examples to see how the arc cosine function works.

In a right triangle, the cosine (θ) of an angle is the ratio of the adjacent side to the hypotenuse. 

Cos Inverse Formula

The domain is R. That is, H. are all real numbers in the range [-1, 1]. A function f(x) has an inverse only if it is bijective (one-one and on). Since cos x is not a one-to-one function, it is not a bijective function, so the arc cosine cannot have R as its range. Therefore, need to restrict the domain to make the cosine function 1:1. The domain of the cosine function can be restricted to [0, π], [π, 2π], [-π, 0], and so on. Get the corresponding branch of arc cosine. Refer to Extramarks for Cos Inverse Formula.

Examples Using Cos Inverse Formula

Example using the Cos Inverse Formula

Example 1: Right triangle ABC, a right angle is at B, base AB = 12 inches, AC = 24 inches, then find the angle A of the triangle.


Hope: Angle A. Given:

Base = 12 inches

hypotenuse = 24 inches

Then use the inverse cos formula.

θ=cos−1(B.H.) A =cos−1(12twenty four)

A =cos−1(0.5)

A =60

Answer: Angle A is60∘

Example 2: Scale a 42″ high building using a 48.5″ ladder. Find the angle the ladder makes with the wall of the building to reach the top.

Location: The angle the ladder makes with the wall of the building. Given the:

Base = 42 inches

hypotenuse = 48.5 inches

Then use the inverse cos formula. 

Then use the inverse cos formula.





Answer: The angle the ladder makes to the wall of the building is 30°.

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FAQs (Frequently Asked Questions)

1. Discuss the cosine graph.

Since the domain and range of the arc cosine function are [-1, 1] and [0, π] respectively, draw the graph of the inverse cos x in the main branch. Knowing the value of the cosine function for a particular angle, plot the points using the same value to create a graph of the arc cosine. If y = cos-1x:

If x = 0 then y = pi/2

If x = 1/2 then y = π/3

If x = 1 then y = 0

If x = -1 then y = π

2. What is the domain of the Cosine function?

The domain of the cosine function is usually restricted to [0, π] and its range remains [-1, 1]. Therefore, the branch of cos inverse x in the range [0, π] is called the main branch. The domain and domain of a function are the domain and domain of its inverse respectively, so the domain of the arc cosine is [-1, 1] and its domain is [0, π]. H. cos inverse x is a function of [-1, 1] → [0, π]. Students must check Cos Inverse Formula on the Extramarks website or mobile application.