Question

the distance between the points (cosx ,sin x )and (sinx - cosx)
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Answer 1

SOLUTION :

TO DETERMINE

The distance between the points

(cosx , sin x ) and (sinx, - cosx)

FORMULA TO BE IMPLEMENTED

The distance between two points (a, b) & (x, y)

$\sf{} = \sqrt{ {(x - a)}^{2} + {(y - b)}^{2} }$

EVALUATION

Here two given points are

(cosx , sin x ) and (sinx, - cosx)

Hence the required distance

$\sf{} = \sqrt{ {( \cos x - \sin x)}^{2} + {( \sin x + \cos x)}^{2} }$

$= \sf{} \sqrt{ { \sin}^{2}x + { \cos}^{2} x - 2 \sin x \cos x + { \sin}^{2}x + { \cos}^{2} x + 2 \sin x \cos x }$

$\sf{} = \sqrt{1 + 1}$

$\sf{} = \sqrt{2}$

FINAL ANSWER

$\boxed {\sf{}{Hence \: the \: required \: distance \: \: = \sqrt{2} \: \: unit }}$

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Locate the following points on the cartesian plane

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