Question

Write the distance between the points A (10 cos θ, 0) and B (0, 10 sin θ).

 

Answer 1

We have to find the distance between A( 10 cos θ,0) and B(0 , 10 sin θ ) .

In general, the distance between A`(x_1 , y_1)`  and B  `(x_2 , y_2)`is given by,

`AB = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`

So,

`AB= sqrt((10 cos θ - 0)^2 + (0 - 10  sin θ)^2)`

     `  = sqrt(10^2 (sin^2 θ + cos^2 θ   ) `

But according to the trigonometric identity,

`sin^2 θ + cos^2 θ = 1`

Therefore,

AB = 10