Math Problem Statement
Convert the polar coordinates (r, φ) with r = 5 and φ = 3π/4 to Cartesian form.
Solution
The problem is asking for the conversion of polar coordinates to Cartesian coordinates.
Given:
To convert from polar to Cartesian coordinates, we use the following formulas:
Step-by-Step Solution:
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Calculate :
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Calculate :
Cartesian Coordinates
The Cartesian form of the point is:
Would you like a more detailed explanation, or do you have any questions?
Here are some related questions for further practice:
- How would you convert from Cartesian to polar coordinates?
- What are the polar coordinates of a point in the third quadrant with the same and angle ?
- How do trigonometric functions behave for different quadrants?
- How would this change if ?
- Can you find the modulus and argument of the complex number in Cartesian form?
Tip: Always check which quadrant your angle falls into to determine the correct signs for and in Cartesian coordinates.
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Math Problem Analysis
Mathematical Concepts
Polar to Cartesian Coordinate Conversion
Trigonometry
Formulas
x = r * cos(φ)
y = r * sin(φ)
Theorems
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Suitable Grade Level
Grades 10-12