Question

find the distance between points
a cos theta ,0 and 0,a sin theta​

Answer 1

To find the distance between two points, we apply distance formula.

Distance formula is given as

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

Here, (x₁, y₁) = (acos∅,0)

and (x₂, y₂) = (0, asin∅)

So, we get distance as

$\sf\sqrt{(0 - acos\theta)^2 + (asin\theta - 0)^2}$

$\sf\sqrt{a^2cos^2\theta + a^2sin^2\theta}$

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

$\sf\sqrt{a^2}$ (It is known that cos²∅ + sin²∅ = 1)

This gives a.

Hence the distance between given two points is a.

Answer 2

$\rule{200}3$

$\huge\tt{TO~FIND:}$

The distance between points a cos theta ,0 and 0,a sin theta.

$\rule{200}3$

$\huge\tt{SOLUTION:}$

Distance formula is √(x2-x1)² + (y2-y1)²

And in here, (x1,y1) = (a cos∅,0) and (x²,y2) = (0,a sin∅)

If we put these value in here,

➠√(0 - acos∅)² + (asin ∅ - 0)²

➠√a² cos²∅ + a²sin²∅

➠√a²(cos²∅ + sin²∅)

➠√a² , (as cos²∅ + sin²∅ = 1)

So, The distance between the two points is a

$\rule{200}3$