Problem 30 - Algebra and Trigonometry Real Mathematics, Real People

Question

Use a graphing utility to find the rectangular coordinates of the point given in polar coordinates. Round your results to two decimal places. $$(8.25,3.5)$$

Step-by-Step Solution

Answer

After calculating and rounding to two decimal places, the rectangular coordinates of the given polar coordinates are expected.

Step 1: Understand Polar Coordinates

In a polar coordinate system, the position of a point is represented by (r, θ), in which r is the distance of the point from the origin and θ is the angle of the point from the positive horizontal axis, measured in a counterclockwise direction.

Step 2: Conversion Formulas

The conversion formulas to transform polar coordinates into rectangular coordinates are: x = r cos θ and y = r sin θ. Here, replace r with 8.25 and θ with 3.5 radians.

Step 3: Compute x-coordinate

Start by calculating the x-coordinate using the formula provided. The x-coordinate can be calculated as: \( x = 8.25 \times \cos(3.5) \).

Step 4: Compute y-coordinate

Next, calculate the y-coordinate, substituting the given values into the conversion formula. The y-coordinate can be calculated as: \( y = 8.25 \times \sin(3.5) \).

Step 5: Round Off Values

Based on the computations done, the x and y coordinates calculated should be rounded off to two decimal places as instructed.