SOLUTION: the distance from the origin to the point (-sin0, cos0) is equivalent to

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Question 1086203: the distance from the origin to the point (-sin0, cos0) is equivalent to
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming the "0"s are supposed to be the greek letter theta theta

The pythagorean identity

%28sin%28theta%29%29%5E2%2B%28cos%28theta%29%29%5E2=1

is the same as

%28-sin%28theta%29%29%5E2%2B%28cos%28theta%29%29%5E2=1

This is because %28-x%29%5E2+=+%28-x%29%2A%28-x%29+=+%28-1%29%2A%28-1%29%2Ax%5E2+=+x%5E2. In short, squaring a negative leads to a positive.

This means that regardless of what theta is, the distance from the origin to the point will always be 1.

The point means that x+=+-sin%28theta%29 and y+=+cos%28theta%29.
So x%5E2%2By%5E2+=+%28-sin%28theta%29%29%5E2%2B%28cos%28theta%29%29%5E2+=+1 which is simply x%5E2%2By%5E2+=+1. This is the equation for the unit circle.

The unit circle is a special circle with radius 1 and centered at the origin.
All such points on the unit circle are exactly 1 unit away from the origin.
The point is located on the unit circle.

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In summary, the answer is 1.