Question

The distance between the points ($\cos$ q, $\sin$ q) and ($\sin$ q, – $\cos$ q) is ___.

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

Answer 1

The correct option is B

$\sqrt{2}$

The distance between the points $(x_1,y_1)$ and $(x_2,y_2)$ is $\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

Applying distance formula, we get:

$Distance=\sqrt{\left(\right({sinq-cosq)}^2+({-cosq-sinq)}^2}$

$=\sqrt{si{n}^{2}q-2sinqcosq+co{s}^{2}q+co{s}^{2}q+2sinqcosq+si{n}^{2}q}$


$=\sqrt{2(co{s}^{2}q+si{n}^{2}q)}=\sqrt{2}(\because co{s}^{2}q+si{n}^{2}q=1)$