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enrotlavaec

enrotlavaec

Answered question

2022-06-14

For f ( t ) = ( cos t 2 , sin 2 t ) what is the distance between f ( π 4 ) and f ( π ) ?

Answer & Explanation

boomzwamhc

boomzwamhc

Beginner2022-06-15Added 17 answers

Step 1
First, let us get the coordinates for each point.
For point f ( π 4 ) , we have
x f = cos ( π 4 ) 2
y f = sin 2 ( π 4 )
As we know, cos ( π 4 ) = sin ( π 4 ) = 1 2
x f = 1 2 2 = 2 4
y f = ( 1 2 ) 2 = 1 2
For point f ( π ) we have
x f = cos ( π ) 2
y f = sin 2 ( π )
We know that cos ( π ) = - 1 and that sin ( π ) = 0 , so
x f = - 1 2
y f = 0
The distance between ( 2 4 ; 1 2 ) and ( - 1 2 ; 0 ) is given by
d 2 = ( 2 4 + 1 2 ) 2 + ( 1 2 ) 2
d 2 = 1 16 ( 2 + 2 ) 2 + 1 4
d 2 = 1 16 ( 2 + 4 2 + 4 ) + 1 4
d 2 = 1 16 ( 6 + 4 2 ) + 1 4
d 2 = 3 + 2 2 8 + 1 4
d 2 = 3 + 2 2 + 2 8
d 2 = 5 + 2 2 8
d = 5 + 2 2 8

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