How do you find vertical asymptote of tangent?

Answer 1

I assume that you are asking about the tangent function, so #tan theta#. The vertical asymptotes occur at the NPV's: #theta=pi/2+n pi, n in ZZ#.

Recall that #tan# has an identity: #tan theta=y/x=(sin theta)/(cos theta)#. This means that we will have NPV's when #cos theta=0#, that is, the denominator equals 0.

#cos theta=0# when #theta=pi/2# and #theta=(3pi)/2# for the Principal Angles. Normally, we have 2 solutions, but the spacing between these 2 angles are the same, so we have a single solution,

#theta=pi/2+n pi, n in ZZ# in radians or
#theta=90+180n, n in ZZ# for degrees.

To find the vertical asymptote of ANY function, we look for when the denominator is 0.

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Answer 2

To find the vertical asymptotes of the tangent function, we need to determine the values of x for which the tangent function is undefined. The tangent function is undefined at values of x where the cosine function is equal to zero. Therefore, the vertical asymptotes of the tangent function occur at x-values where the cosine function equals zero. These values can be found by solving the equation cos(x) = 0. The solutions to this equation are x = (2n + 1)π/2, where n is an integer. These values represent the vertical asymptotes of the tangent function.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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