Question 1086203
<font color="black" face="times" size="3">I'm assuming the "0"s are supposed to be the greek letter theta {{{theta}}}


The pythagorean identity


{{{(sin(theta))^2+(cos(theta))^2=1}}}


is the same as 


{{{(-sin(theta))^2+(cos(theta))^2=1}}}


This is because {{{(-x)^2 = (-x)*(-x) = (-1)*(-1)*x^2 = x^2}}}. 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 *[Tex \Large \left(-\sin(\theta),\cos(\theta)\right)] will always be 1. 


The point *[Tex \Large \left(-\sin(\theta),\cos(\theta)\right)] means that {{{x = -sin(theta)}}} and {{{y = cos(theta)}}}. 
So {{{x^2+y^2 = (-sin(theta))^2+(cos(theta))^2 = 1}}} which is simply {{{x^2+y^2 = 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  *[Tex \Large \left(-\sin(\theta),\cos(\theta)\right)] is located on the unit circle.


-----------------------------------------------------------------------


In summary, the answer is 1.</font>