If r sinθ = sqrt 3 and r cosθ = 1, the value of r and θ are?

r sinθ = \(\sqrt {3 }\)

r cosθ = 1

squaring and adding

⇒ r² (sin²θ + cos²θ) = 4

⇒ r² = 4    (because sin²θ + cos²θ = 1)

\(\frac{r\;sinθ}{r\;cosθ}\) = \(\sqrt { 3}\) ⇒ tanθ = \(\sqrt {3 }\)

⇒ θ = 60°,  r = 2