4.5.4 Graph of the inverse tangent function
Chapter 4: Chapter 4 · MATHEMATICS-VOLUME 1 · EN medium
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. . Graph of the inverse tangent function tan is a function with the entire real line −∞∞ as its domain and whose range is . Note that the tangent function is undefined at - p and at p . So, the graph of y tan lies strictly between the two lines y = − π and y = π , and never touches these two lines. In other words, the two lines y = − π and y = π are horizontal asymptotes to y tan Fig. . and Fig. . show the graphs of y = tan in the domain − and y tan in the domain ( −∞∞ , respectively. Fig. . Fig. . Note (i) The inverse tangent function is strictly increasing and continuous on the domain −∞∞ (ii) The graph of y tan passes through the origin.
📖 Class 12 Mathematics English Volume 1 2025 Edition www.tntextbooks.in · Page 153
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. . Graph of the inverse tangent function tan is a function with the entire real line −∞∞ as its domain and whose range is . Note that the tangent function is undefined at - p and at p .
So, the graph of y tan lies strictly between the two lines y = − π and y = π , and never touches these two lines. In other words, the two lines y = − π and y = π are horizontal asymptotes to y tan Fig. . and Fig.
. show the graphs of y = tan in the domain − and y tan in the domain ( −∞∞ , respectively. Fig. .
Fig. . Note (i) The inverse tangent function is strictly increasing and continuous on the domain −∞∞ (ii) The graph of y tan passes through the origin. (iii) The graph is symmetric with respect to origin and hence, y tan is an odd function.
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