For <mstyle displaystyle="true"> f ( t )

Micaela Simon

Micaela Simon

Answered question

2022-06-21

For f ( t ) = ( sin t - cos t , t 2 ) what is the distance between f(2) and f(5)?

Answer & Explanation

Lilliana Burton

Lilliana Burton

Beginner2022-06-22Added 19 answers

Step 1
f ( t ) = ( sin t - cos t , t 2 )
f ( 2 ) = ( sin 2 - cos 2 , 4 )
f ( 5 ) = ( sin 5 - cos 5 , 25 )
Step 2
By Pythagoras, the difference between these points is;
distance ( sin 5 - sin 2 ) 2 + ( - cos 5 - - cos 2 ) 2
( sin 5 - sin 2 ) 2 + ( - cos 5 + cos 2 ) 2
sin 2 5 - 2 sin 5 sin 2 + sin 2 2 + cos 2 5 - 2 cos 5 cos 2 + cos 2 2
sin 2 5 + cos 2 5 - 2 sin 5 sin 2 - 2 cos 5 cos 2 + cos 2 2 + sin 2 2
1 - 2 sin 5 sin 2 - 2 cos 5 cos 2 + 1
2 - 2 sin 5 sin 2 - 2 cos 5 cos 2
2 - 2 ( sin 5 sin 2 + cos 5 cos 2 )
2 - 2 cos ( 5 + 2 )
2 - 2 cos ( 7 )

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?