https://file.aiquickdraw.com/mathbot/file/1729712835947616c369g.jpg

To convert polar coordinates \((-4, -2\pi)\) into rectangular coordinates \((x, y)\), we use the following formulas:

\[
x = r \cdot \cos(\theta)
\]
\[
y = r \cdot \sin(\theta)
\]
Where:
- \( r = -4 \) (the radial distance)
- \( \theta = -2\pi \) (the angle in radians)

### Step 1: Calculate \(x\)
\[
x = -4 \cdot \cos(-2\pi)
\]
Since \( \cos(-2\pi) = \cos(2\pi) = 1 \):
\[
x = -4 \cdot 1 = -4
\]

### Step 2: Calculate \(y\)
\[
y = -4 \cdot \sin(-2\pi)
\]
Since \( \sin(-2\pi) = \sin(2\pi) = 0 \):
\[
y = -4 \cdot 0 = 0
\]

### Final Rectangular Coordinates:
\[
(x, y) = (-4, 0)
\]

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. What happens if the angle is in degrees instead of radians?
2. How does a negative radius affect the rectangular coordinates?
3. Can you convert rectangular coordinates back to polar coordinates?
4. What are the rectangular coordinates of \((-4, \pi)\)?
5. How does \(\cos(\theta)\) and \(\sin(\theta)\) behave for different values of \(\theta\)?

**Tip**: Remember that the cosine and sine of angles at multiples of \(\pi\) often produce simple values like 0, 1, or -1.

Find the rectangular coordinates of the point that has polar coordinates (-4, -2π).

Learn how to convert polar coordinates (-4, -2π) into rectangular coordinates using trigonometric functions. This problem involves applying the cosine and sine functions for multiples of π. Suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation