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