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rcmango
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Homework Statement
why does cos x diverge?
Homework Equations
The Attempt at a Solution
is it because it never stops continuing to infinity? it just oscilates until 1?
and does sinx also diverge?
thanks
rcmango said:Homework Statement
why does cos x diverge?
Homework Equations
The Attempt at a Solution
is it because it never stops continuing to infinity? it just oscilates until 1?
and does sinx also diverge?
thanks
rcmango said:yes, do they both diverge? as to, going to infinity and never stopping.
also, is this because they have an upper and lower bound, for both, as in -1 and 1 correct?
When we say that Sinx and Cosx diverge, it means that the values of these trigonometric functions approach infinity or negative infinity as the input (x) approaches a certain value or as x increases or decreases without bound.
Sinx and Cosx diverge because they are not defined for certain values of x. For example, the value of Sinx is undefined for x = (2n + 1)π/2 where n is any integer, and the value of Cosx is undefined for x = nπ where n is any integer. This leads to an infinite or undefined output, causing the functions to diverge.
We can determine when Sinx and Cosx will diverge by looking at the values of x that make the functions undefined, as mentioned in the previous answer. These values are known as the vertical asymptotes of the functions and indicate where the functions will diverge.
Yes, there is a difference between Sinx and Cosx diverging. While Sinx diverges to both positive and negative infinity as x approaches a vertical asymptote, Cosx only diverges to positive or negative infinity depending on the quadrant of the vertical asymptote. For example, if the vertical asymptote is in the first or fourth quadrant, Cosx will diverge to positive infinity, but if it is in the second or third quadrant, Cosx will diverge to negative infinity.
Knowing when Sinx and Cosx diverge can help us accurately graph these functions. The vertical asymptotes indicate where the functions will approach infinity or negative infinity, and this can help us determine the shape and direction of the graph. Without this knowledge, the graph may not be accurate and may not show the complete behavior of the functions.