Question

If x = r cos θ, y = r sin θ then x² + y² is equal to ______.

Options

• r²

• 1

• `1/r^2`

• r

Answer 1

If x = r cos θ, y = r sin θ, then x² + y² is equal to r².

Explanation:

If x = r cosθ and y = r sinθ, then:

x² = (r cos θ)² = r² cos² θ

y² = (r sin θ)² = r² sin² θ

x² + y² = r² cos² θ + r² sin² θ

x² + y² = r² (cos² θ + sin² θ)

Since sin² θ + cos² θ = 1

x² + y² = r² (1)

x² + y² = r²