Question

the distance between ( cos theta , sin theta ) and ( sintheta , - cos theta) is what?

Answer 1

d=underroot {(cosa -sina)^2 +(sina+cosa)^2}
={ cos^2a + sin^2a+ 2sina cosa+sin^2a + cos^2a-2sina cosa}
={1+1}
=root2

Answer 2

$\huge\boxed{\texttt{\fcolorbox{Red}{yellow}{Hey Mate!!!!}}}$

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Here is your answer.

As we know the formula
The distance between them is
$d {}^{2} = ( \cos( \alpha ) - \sin( \alpha ) ) {}^{2} + ( \sin( \alpha ) - ( - \cos( \alpha ) )) {}^{2} \\ d {}^{2} = \cos {}^{2} ( \alpha ) + \sin {}^{2} ( \alpha ) - 2 \cos( \alpha ) \sin( \alpha ) + \sin {}^{2} ( \alpha ) + \cos {}^{2} ( \alpha ) + 2 \sin( \alpha ) \cos( \alpha ) \\ \\ d {}^{2} = 1 + 1 \\ \\ d {}^{2} = 2 \\ \\ \\ d = \sqrt{2}$
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