Question

What is $(12,5)$ in polar co-ordinates?

• A. $(13,{22.6}^o)$
• B. $(13,{66.2}^o)$
• C. $(31,{22.6}^o)$
• D. $(31,{66.2}^o)$

Answer 1

Answer: (A)

$(13,{22.6}^o)$

Form of the polar co ordinates is $(R,\theta )$

where $R=\sqrt{x^2+y^2}$

$⟹\sqrt{{12}^2+5^2}=13$

And where $\theta ={tan}^{-1}\left(\frac{y}{x}\right)$

$⟹\theta ={tan}^{-1}\left(\frac{5}{12}\right)$

$⟹\theta ={22.6}^{\circ }$

Final answer $(13,{22.6}^{\circ })$