Question

The distance between the points \( (2\cos\theta, 0) \) and \( (0, 2\sin\theta) \) is:

• A. \( 1 \)
• B. \( 2 \)
• C. \( 3 \)
• D. \( 4 \)

Hint:

The Pythagorean identity \( \cos^2\theta + \sin^2\theta = 1 \) simplifies many distance calculations.

Answer 1

The Correct Option is D

Step 1: Use the distance formula The distance between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Step 2: Substitute values Given points: - \( (2\cos\theta, 0) \) - \( (0, 2\sin\theta) \) \[ d = \sqrt{(0 - 2\cos\theta)^2 + (2\sin\theta - 0)^2} \] \[ = \sqrt{(2\cos\theta)^2 + (2\sin\theta)^2} \] \[ = \sqrt{4\cos^2\theta + 4\sin^2\theta} \] \[ = \sqrt{4(\cos^2\theta + \sin^2\theta)} \] \[ = \sqrt{4(1)} \] \[ = \sqrt{4} = 2 \] Thus, the correct answer is \( 2 \).