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Roland Waters

Roland Waters

Answered question

2022-06-20

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

Answer & Explanation

plodno8n

plodno8n

Beginner2022-06-21Added 17 answers

Step 1
cos ( π 4 ) = 2 2
sin ( π 4 ) = 2 2
sin π = 0
cos π = - 1
Let's calculate f ( π 4 ) and f ( π )
f ( t ) = ( sin 2 t , cos 2 t )
f ( π 4 ) = ( sin 2 ( π 4 ) , cos 2 ( π 4 ) )
= ( ( 2 2 ) 2 , ( 2 2 ) 2 )
= ( 1 2 , 1 2 )
f ( π ) = ( sin 2 ( π ) , cos 2 ( π ) )
= ( 0 , 1 )
The distance between 2 points ( x 1 , y 1 ) and ( x 2 , y 2 ) is
d = ( x 2 - x 1 ) 2 + y 2 - y 1 2 )
The distance is
= ( 0 - 1 2 ) 2 + ( 1 - 1 2 ) 2
= 1 4 + 1 4
= 2 2 = 0.707

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