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Hello to all,

Okay...so I have chosen a math IA topic after finding out that my previous topic was a bit too complex and it was out of the syllabus.  But, now for this new topic, I'm stuck with this one part. I have attached a file that has a picture as to what I'm talking about. Its basically a model for a blood vessel. Now I want to write and equation for the total energy loss which could be modeled by E = E1 + E= kl1/r14 + kl2/r24. However when I try solving for land l2 in terms of θ, and then substituting it within the equation, I end up with a quite odd looking function, which I can't graph. I think I'm doing something wrong but I just don't get what it is.

The equations I am getting for  land l2 in terms of θ, are:

- l2 = 20/sinθ or 20 -  l1/cos θ

- l1 = - l2 (cos θ) + 20 or 20 - 20(tanθ)/tanθ

Oh and the values I used for the variables are:

a = 20mm (2cm), b = 20mm (2cm), r1=6mm, r2= 2mm


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I didn't check if your math is correct, but 1/sin, 1/cos, and 1/tan are the reciprocals of sin, cos, tan, which have the proper names of cosecant (csc = 1/sin), secant (sec = 1/cos) and cotangent (cot = 1/tan). These are explored briefly in HL. They have different shapes than the sin/cos/tan because every time the sin/cos/tan is 0 (eg sin 0, sin pi, cos pi/2) the reciprocal 1/0 is undefined and the graph has an asymptote instead of a root. You should see what the asymptotes are in the individual reciprocal trig functions (with the respective shifts and stretches) and determine which angles return answers that doesn't make sense. My guess is that the answers will be fine for angles less than pi/2 radians.

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