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Polar ↔ Cartesian
x = r cos θ, y = r sin θ; r = √(x² + y²), θ = tan⁻¹(y/x)
Where: r = radius, θ = angle, x = Polar ↔ Cartesian
Solved example
Given: r = 7, theta = 45°
Find: x (Polar ↔ Cartesian)
- Formula: x = r·cos(θ)
- Substitute the values: x = 7·cos(45°)
- Result: x = 4.949747
Answer: x = 4.949747
Calculator
How to calculate Polar ↔ Cartesian
- Write down the formula: x = r cos θ, y = r sin θ; r = √(x² + y²), θ = tan⁻¹(y/x).
- Note the known values (r, θ).
- Substitute them and simplify to find x.
- Use the calculator above to solve for any letter.
Frequently asked questions
What is the formula for Polar ↔ Cartesian?
The formula is x = r cos θ, y = r sin θ; r = √(x² + y²), θ = tan⁻¹(y/x), where r = radius, θ = angle, x = Polar ↔ Cartesian.
What is Polar ↔ Cartesian when r = 7, theta = 45°?
x = 4.949747. Substitute the values into x = r cos θ, y = r sin θ; r = √(x² + y²), θ = tan⁻¹(y/x) and simplify.