Question

the distance between the points (cos theta, sin theta) and( sin theta minus cos theta) is

Answer 1

Answer:

Distance between the points is $\sqrt2$

Step-by-step explanation:

The given points are

$(\cos\theta,\sin\theta),((\sin\theta,-\cos\theta)$

The distance of two points is given by the formula

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

Substituting the values, we get

$d=\sqrt{(\sin\theta-\cos\theta)^2+(-\cos\theta-\sin\theta)^2}\\\\d=\sqrt{\sin^2\theta+\cos^2\theta-2\sin\theta\cos\theta+\sin^2\theta+\cos^2\theta+2\sin\theta\cos\theta}\\\\d=\sqrt{2(\sin^2\theta+\cos^2\theta)}\\\\d=\sqrt2$

Hence, the distance between the points is $\sqrt2$

Answer 2

Answer:

root 2 is the correct answer