<transcript><audio_34>in fact this is the problem with any sinusoid or core sinusoid as you might want to call it just a sine or cosine term can never take you all over the real axis among the trigonometric functions the sine and cosine functions do not</transcript><transcript><audio_35>take you all over the all over the real axis which function takes you all over the real axis the tangent function or the cotangent function so somehow we need a cotangent or a</transcript><transcript><audio_36>now how do we get a tangent function you cannot get a tangent function by so you can get a tangent function if you divide that's another you see if you divide a sine function by a cosine function or</transcript><transcript><audio_37>a cosine function by a sine function you get a tangent function that's another reason why you would want some kind of proper rational function of z to replace</transcript><transcript><audio_38>and in fact if we take tan tangent we have the answer tan omega by 2 when omega goes from minus pi to plus pi tan omega by 2 would indeed run all the way from minus to plus infinity</transcript><transcript><audio_39>so if we can go from here you see we should make we should try</transcript><caption><image_40>The image is a whiteboard with a hand holding a pen and writing on it. The text on the whiteboard is written in black ink and appears to be a mathematical equation. The equation is written as "7 = =" and is written on the left side of the board. On the right side, there is a logo of the Indian government, which is a shield with a crown on top and the words "CDEEP" written in the center. Below the logo, there are two lines of text, one representing the equation and the other representing the value. The background of the image is plain white.</caption> in fact this is the problem with any sinusoid or core sinusoid as you might want to call it just a sine or cosine term can never take you all over the real axis among the trigonometric functions the sine and cosine functions do not take you all over the all over the real axis which function takes you all over the real axis the tangent function or the cotangent function so somehow we need a cotangent or a now how do we get a tangent function you cannot get a tangent function by so you can get a tangent function if you divide that's another you see if you divide a sine function by a cosine function or a cosine function by a sine function you get a tangent function that's another reason why you would want some kind of proper rational function of z to replace and in fact if we take tan tangent we have the answer tan omega by 2 when omega goes from minus pi to plus pi tan omega by 2 would indeed run all the way from minus to plus infinity so if we can go from here you see we should make we should try
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