Question

Find the corresponding rectangular coordinates for the point (,
theta) = (√2, 2.41).

Answer 1

To find the rectangular coordinates for the point with polar coordinates (\( \sqrt{2} \), 2.41), calculate x = \( \sqrt{2} \) cos(2.41) and y = \( \sqrt{2} \) sin(2.41) using a calculator to obtain the cosine and sine values.

Step-by-step explanation:

To convert polar coordinates to rectangular coordinates, we use the formulas x = r cos(\( \theta \)) and y = r sin(\( \theta \)), where r is the radius (distance from the origin) and \( \theta \) is the angle in radians from the positive x-axis.

For the point with polar coordinates (\( \sqrt{2} \), 2.41), we calculate the rectangular coordinates as follows:

• x-coordinate: x = \( \sqrt{2} \) cos(2.41)
• y-coordinate: y = \( \sqrt{2} \) sin(2.41)

Using a calculator to find the cosine and sine of 2.41 radians, we can then compute the respective x and y values.