Question

The distance between the points $(cos\theta ,sin\theta )$ and $(sin\theta ,-cos\theta )$ is

• A. $\sqrt{3}$
• B. $\sqrt{2}$
• C. 2
• D. 1

Answer 1

The correct option is

A

$\sqrt{2}$

By using distance formula, we get

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

$=\sqrt{(sin\theta -cos\theta {)}^2+(-cos\theta -sin\theta {)}^2}$
$=\sqrt{si{n}^2\theta -2sin\theta cos\theta +co{s}^2\theta +co{s}^2\theta +2sin\theta cos\theta +si{n}^2\theta }$
$=\sqrt{(si{n}^2\theta +co{s}^2\theta )+(co{s}^2\theta +si{n}^2\theta )}$
$=\sqrt{1+1}=\sqrt{2}$