Mathematics · Ch 4 — Inverse Trigonometric Functions

The Graph of the Cotangent Function

4.8.1

The Graph of the Cotangent Function

Cotangent is continuous on $(0,2\pi)\setminus\{\pi\}$ . In Quadrants I and III it is positive; in Quadrants II and IV it is negative. Piece by piece it FALLS: from $+\infty$ to $0$ over $\left(0,\tfrac{\pi}2\right]$ ; from $0$ to $-\infty$ over $\left[\tfrac{\pi}2,\pi\right)$ ; from $+\infty$ to $0$ again over $\left(\pi,\tfrac{3\pi}2\right]$ ; and from $0$ to $-\infty$ over $\left[\tfrac{3\pi}2,2\pi\right)$ — cotangent has NEITHER a maximum nor a minimum. …

Figure 4.27Graph of y = cot x on (0, 2pi) excluding pi: a decreasing branch over (0, pi) from infinity through (pi/2, 0) to minus infinity, repeated over (pi, 2pi) through (3pi/2, 0); vertical asymptote at x = pi.

Fig. 4.27 — Graph of y = cot x on (0, 2pi) excluding pi: a decreasing branch over (0, pi) from infinity through (pi/2, 0) to minus infinity, repeated over (pi, 2pi) through (3pi/2, 0); vertical asymptote at x = pi.

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your textbook's own diagram.

What this figure shows. Two steeply falling branches, each dropping from $+\infty$ near its left asymptote to $-\infty$ near its right asymptote, at $x=0,\pi,2\pi$ . …

Figure 4.28Graph of y = cot x over its entire domain: a periodic decreasing branch over each interval (n*pi, (n+1)*pi) passing through zero at the midpoint; vertical asymptotes at x = n*pi.

Fig. 4.28 — Graph of y = cot x over its entire domain: a periodic decreasing branch over each interval (n*pi, (n+1)*pi) passing through zero at the midpoint; vertical asymptotes at x = n*pi.

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your textbook's own diagram.

What this figure shows. The Fig. 4.27 pair of falling branches repeated at every interval of length $\pi$ , with vertical asymptotes at every integer multiple of $\pi$ . …

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