Question

i) In the space below, give a rough sketch of the graph of the function y = tan-'(x). ii) By looking at the graph you just drew, what y value does the function y = tan-(x) approach as x gets larger and larger (in the positive direction)? Explain your reasoning. An answer without an explanation will be granted no points.

Answer 1

DATE : | । PAGE NO.: tan' (2) ਹੈਂ "/t % - 4 ਟੇ , 지

ii) This graph keeps on repeating on every pi interval, so as x gets larger and larger then y tends to form an aymptote. At (n+1)π/2 where n belongs {0,2,4,6,8…} the graph of tan forms a asymptote and it tends to infinite.. and the range of tan inverse x is -infinite to infinite so it can be said that the value of tan inverse infinite is (n+1)π/2 that is at π/2, 3π/2, 5π/2……

$\tiny tan\frac{\pi }{2}=\infty \Rightarrow \frac{\pi}{2}=tan^{-1}(\infty)\\or\\\\tan^{-1}=tan^{-1}(tan\frac{\pi}{2})=\frac{\pi}{2}$

similarly for all (n+1)π/2 it can be shown.

Hope this helps!