Question

The distance between the points (cos 30°, sin 30°) and (cos 60°, –sin 60°) is ______.

विकल्प

• 0 unit

• `sqrt(3)` units

• 1 unit

• `sqrt(2)` units

Answer 1

The distance between the points (cos 30°, sin 30°) and (cos 60°, –sin 60°) is `underlinebb(sqrt2  units)`.

Explanation:

First, we need to find the numerical values for the given trigonometric expressions.

Point 1: (cos 30°, sin 30°) = `(sqrt3/2, 1/2)`

Point 2: (cos 60°, –sin 60°) = `(1/2, -sqrt3/2)`

Apply the distance formula:

The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by:

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

= `sqrt((1/2 - sqrt(3)/2)^2 + (-sqrt3/2 - 1/2)^2`

= `sqrt((1 - 2sqrt3 + 3)/4 + (3 + 2sqrt3 + 1)/4)`

= `sqrt((4 - 2sqrt3)/4 + (4 + 2sqrt3)/4)`

= `sqrt(((4 - 2sqrt3) + (4 + 2sqrt3))/4)`

= `sqrt(8/4)`

= `sqrt(2)`