Cos Inverse Formula

About Cos Inverse Formula

The inverse trigonometric function inverse cosine is very useful. It is the inverse function of the trigonometric function cosine, and is expressed as cos-1(x) in mathematics (x). It's worth noting that inverse cosine isn't the same as cos x's reciprocal. sin-1x, cos-1x, tan-1x, csc-1x, sec-1x, cot-1x are the six inverse trigonometric functions.

By using the value of trigonometric ratio cos x, inverse cosine is used to get the angle measure.

Define Inverse Cosine:

The inverse function of the cosine function is inverse cosine. It is a significant inverse trigonometric function. arccos x is another way to write cos inverse x. If y = cos x, and x = cos-1, then (y)

  1. cos 0 = 1 ⇒ 0 = cos-1(1)
  2. cos π /3 = 1/2 ⇒ π /3 = cos -1(1/2)
  3. cos π /2 = 0 ⇒ π /2 = cos-1(0)
  4. cos π = -1 ⇒ = cos -1(-1)

The ratio of an angle's adjacent side to the hypotenuse in a right-angled triangle is cos = (adjacent side) / hypotenuse (hypotenuse). = cos-1[(adjacent side) / (hypotenuse)], according to the concept of inverse cosine.

Hence, Inverse cosine is used to find out unknown angles in a right-angled triangle.

Also Check: Diffrence Between area and Volume | Diffrence Between Cube and Cuboid | Diffrence Between Mean, Median Mode

Properties of Inverse Cosine

The inverse cosine function's features and formulas are listed below. These are quite useful in solving trigonometry issues involving cos inverse x.

cos(cos-1x) = x only when x ∈ [-1, 1] (When x ∉ [-1, 1], cos(cos-1x) is not defined)

cos-1(cos x) = x, only when x ∈ [0, π] (When x ∉ [0, π], apply the trigonometric identities to find the equivalent angle of x that lies in [0, π])

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Cos Inverse Formula
Cos Inverse Formula

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