wyattrosier wyattrosier
  • 07-04-2024
  • Mathematics
contestada

x=5 tan t, y = 4 sec t; 0≤t≤2

How would I even convert the sec here?

x5 tan t y 4 sec t 0t2 How would I even convert the sec here class=

Respuesta :

dashataran
dashataran dashataran
  • 07-04-2024

Answer:

[tex]\tan t=\dfrac{x}{5}\\\\\text{Now,}\\\sec^2t-\tan^2t=1\\\\\text{or, }\sec^2t-\dfrac{x^2}{5^2}=1\\\\\text{or, }\sec^2t=1+\dfrac{x^2}{25}\\\\\text{or, }\sec^2t=\dfrac{x^2+25}{25}\\\\\therefore\ \sec t=\dfrac{\sqrt{x^2+25}}{5}[/tex]

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