What is the Value of Sin and Cos Infinity (2024)

FAQs

What is the Value of Sin and Cos Infinity? ›

Therefore, it can be said that the values of sin and cos infinity range between -1 to 1 and no exactly defined values are found.

i.e., The value of sin x and cos x always lies in the range of -1 to 1. Also, ∞ is undefined thus, sin(∞) and cos(∞) cannot have exact defined values. However, sin x and cos x are periodic functions having a periodicity of (2π). Thus, the value of sin and cos infinity lies between -1 to 1.

We know that for sin x, and cos x their range is between -1 and 1 and so for the infinite limit their value oscillates between -1 and 1 finding their exact value is not possible and thus their lint at infinity is undefined.

The limit of cos(x) as n approaches infinity does not exist because the cosine function oscillates between -1 and 1, and does not approach any specific value as x gets larger.

As many have already correctly answered, the cosine of infinity has no value.

Infinity is not a number. So, you cannot add or subtract it. It's more likely that the quantity you refer to as infinity is an expression that gets larger than any number you can give.. We use the terms infinity and - infinity not as a number but to say that it gets arbitrarily large.

Looking out from a vertex with angle θ, sin(θ) is the ratio of the opposite side to the hypotenuse , while cos(θ) is the ratio of the adjacent side to the hypotenuse . No matter the size of the triangle, the values of sin(θ) and cos(θ) are the same for a given θ, as illustrated below.

English. This trig identity shows that a combination of sine and cosine functions can be written as a single sine function with a phase shift. acost+bsint=√a2+b2sin(t+tan−1ab) ⁡ t + b sin ⁡ t = a 2 + b 2 sin ⁡ ( t + tan − 1 ⁡

Is cosine infinite? ›

More modern definitions express the sine and cosine as infinite series, or as the solutions of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers.

Answer and Explanation:

If the limit diverges then sin of infinity does not exist. Hence, lim x → ∞ ( cos ⁡ diverges. Therefore, ⁡ does not exist.

cos^-1(infinity) = the angle whose cosine = infinity. it doesn't exist, as all angles have cosines between -1 and +1.

An infinite limit has a specific meaning, in that the function is eventually greater or smaller than any finite number. Since the sine does not exhibit this behaviour, its limit at infinity is undefined.

In this case, the limit does exist, as in the limit is infinity, but it is still considered undefined because the limit is not a finite value. Another reason might be that the function oscillates so that one particular value doesn't exist. An example of this would be lim x → 0 f ( x ) = sin ⁡ ( 1 x ) .

This kind of attenuation is just unsound; the limit of sin(x) as x goes to infinity does not exist, and the function does not converge in any sense.

There is the concept of extended real numbers. This concept accepts infinity as a number that you can do arithmetic operations on. Like infinity*infinity = infinity. But even in this context, infinity/infinity in most literature remains undefined.