Question

find the distance between the points (cos theta, -sin theta) and ( -cos theta, sin theta) )

Answer 1

Answer:

Step-by-step explanation:

The given points are:

$(cos{\theta},-sin{\theta})$ and $(-cos{\theta},sin{\theta})$

The distance formula is given as:

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

Now, the distance between the points $(cos{\theta},-sin{\theta})$ and $(-cos{\theta},sin{\theta})$are:

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

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

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

$\sqrt{4sin^2{\theta}+4cos^2{\theta}}$

$\sqrt{4(sin^2{\theta}+cos^2{\theta})}$

$\sqrt{4}$

$2$ which is the required distance.