Question

What is the distance between the point a sin theta minus cos theta, 0 and b 0 comma sin theta + cos theta

Answer 1

Answer:

$=\sqrt{2}$

Step-by-step explanation:

Distance between two points

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

Given::

$A(sin\theta-cos\theta,0),\:B(0,sin\theta+cos\theta)$

Distance between A and B

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

$=\sqrt{ {(sin\theta-cos\theta-0)}^2+{(0-(sin\theta+cos\theta))}^2}}$

$=\sqrt{sin^2{\theta}+cos^2{\theta}-2sin\theta.cos\theta+sin^2{\theta}+cos^2{\theta}+2sin\theta.cos\theta}$

$=\sqrt{1-2sin\theta.cos\theta+1+2sin\theta.cos\theta}$

$=\sqrt{2}$