Question

Use technology to convert the polar coordinates (5, 6.1) to rectangular coordinates.

O (0.98, -0.18)
O (0.98, 0.18)
O (4.92, -0.91)
O (4.92, 0.91)

Answer 1

(c) (4.92, -0.91)

Explanation:

The conversion shown in the attached uses the complex number features of the calculator, so the y-coordinate is shown as an imaginary value. Rounded to 2 decimal places the conversion is ...

(r; θ) ⇔ (x, y)

(5; 6.1) ⇔ (4.92, -0.91)

__

The correct answer choice can be made without the use of technology. The sum of the magnitudes of the values of x and y must not be less than r, eliminating the first two choices. The angle 6.1 radians is near the angle 6.28 radians (2π), so is almost 360°. It will be a 4th-quadrant angle, so its y-component will be negative (eliminating the last choice).

The only viable choice for polar coordinates of radius 5 and angle 6.1 radians is the third choice: (4.92, -0.91).

__

Additional comment

The angle given has no units, so we assume it is given in radians. A calculator can only give a proper answer if it is set to radians mode for angles.