MHB Graph $r(t)$ for t = $\pi/4$: Position and Tangent Vectors

[ineedhelpnow]

$r(t)=sin(t)$i $+ 2cos(t)$j
$t= \pi/4$

sketch the position vector and the tangent vector

$r'(t)=cos(t)$i $- 2sin(t)$j

$r(\pi/4)= \frac{\sqrt{2}}{2}$i $+ \sqrt{2}$j

$r'(\pi/4)= \frac{\sqrt{2}}{2}$i $- \sqrt{2}$j

$\left\langle \frac{\sqrt{2}}{2}, \sqrt{2} \right\rangle$
$\left\langle \frac{\sqrt{2}}{2}, - \sqrt{2} \right\rangle$

can someone help me graph these. the original equation is the graph of a ellipse/circle from -1 to 1 on the x-axis and -2 to 2 on the y axis

 

[I like Serena]

$r(t)=sin(t)$i $+ 2cos(t)$j
$t= \pi/4$

sketch the position vector and the tangent vector

$r'(t)=cos(t)$i $- 2sin(t)$j

$r(\pi/4)= \frac{\sqrt{2}}{2}$i $+ \sqrt{2}$j

$r'(\pi/4)= \frac{\sqrt{2}}{2}$i $- \sqrt{2}$j

$\left\langle \frac{\sqrt{2}}{2}, \sqrt{2} \right\rangle$
$\left\langle \frac{\sqrt{2}}{2}, - \sqrt{2} \right\rangle$

can someone help me graph these. the original equation is the graph of a ellipse/circle from -1 to 1 on the x-axis and -2 to 2 on the y axis

Let's see...

[desmos="-4,4,-3,3"]x^2+y^2/4=1;y=2x\left\{0<x<\frac{\sqrt{2}}{2}\right\};y=2\sqrt{2}-2x\left\{\frac{\sqrt{2}}{2}<x<\sqrt{2}\right\}[/desmos]

 

[ineedhelpnow]

ok so i literally posted this question on a bunch of different sites and once again MHB was the first to succeed :) thanks ILS!