enrotlavaec

2022-06-26

For $f\left(t\right)=\left(\mathrm{sin}t-\mathrm{cos}t,t\right)$ what is the distance between $f\left(\frac{\pi }{4}\right)$ and $f\left(\pi \right)$ ?

Nia Molina

Expert

Step 1
$f\left(\frac{\pi }{4}\right)=\left(\mathrm{sin}\left(\frac{\pi }{4}\right)-\mathrm{cos}\left(\frac{\pi }{4}\right),\frac{\pi }{4}\right)=\left(0,\frac{\pi }{4}\right)$
$f\left(\pi \right)=\left(\mathrm{sin}\left(\pi \right)-\mathrm{cos}\left(\pi \right),\pi \right)=\left(1,\pi \right)$
Step 2
The distance is:
$d=\sqrt{\left(1-0\right)²+\left(\pi -\frac{\pi }{4}\right)²}$
Answer: $\approx 2.56$

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