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^2θ + cos^2θ)`

But according to the trigonometric identity,

`sin^2θ + cos^2θ = 1`

Therefore,

AB = 10