Question

Find the distance between the pair of points ( sin , − cos ) and (− cos , sin )​

Answer 1

Correct question :

Find the distance between the pair of points ( sinA , − cosA ) and (− cosA , sinA )

Given :

Two points

1. ( sinA , -cosA )
2. ( -cosA , sinA)

To find :

Distance between two points

Formula used :

$\sf D \: = \: \sqrt{(x_2-x_1)^2 \: + \: (y_2-y_1)^2}$

Solution :

In given points,

• x₁ = sinA
• y₁ = -cosA
• x₂ = -cosA
• y₂ = sinA

$\sf \implies D \: = \: \sqrt{( -cosA - sinA)^2 \: + \: (sinA -(-cosA))^2}$

$\sf \implies D \: = \: \sqrt{( - \: (cosA + sinA))^2 \: + \: (sinA + cosA)^2}$

$\sf \implies D \: = \: \sqrt{ \: (cosA + sinA)^2 \: + \: (sinA + cosA)^2}$

$\sf \implies D \: = \: \sqrt{\: (sinA + cosA)^2 \: + \: (sinA + cosA)^2}$

$\sf \implies D \: = \: \sqrt{\: 2(sinA + cosA)^2 \: }$

$\sf \implies D \: = \: (sinA + cosA) \sqrt{2}$

ANSWER :

Distance = (sinA + cosA)√2