[tex](10.05\text{, 3.04 \rparen}[/tex]
Explanation
A Cartesian coordinate system in two dimensions is defined by an ordered pair of perpendicular lines (axes),this system specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, ( x, y)
and polar form denifes the point in termsf the distnace to the orgin (0,0) and teh angle formed with respect to x-positive axis
)
so, to convert from Cartessiang to polar formwe need to use the formula
[tex]\begin{gathered} r=\sqrt{x^2+y^2} \\ \theta=\tan^{-1}(\frac{y}{x}) \end{gathered}[/tex]
Step 1
a) let
[tex]\begin{gathered} (x,y)\Rightarrow(-10,1) \\ so \\ x=-10 \\ y=1 \end{gathered}[/tex]
now, replace in the formula
i) magnitude ( r)
[tex]\begin{gathered} r=\sqrt{x^2+y^2} \\ replace \\ r=\sqrt{(-10)^2+(1^2)}=\sqrt{101} \\ r=10.05 \end{gathered}[/tex]
ii) angle
[tex]\begin{gathered} \theta=\tg^{-1}(\frac{y}{x}) \\ replace \\ \theta=\tan^{-1}(\frac{1}{-10}) \\ \theta=-0.0999\text{ radians} \\ or \\ \theta=-0.0999\text{rad}\imaginaryI\text{ans+}\pi \\ \theta=3.04\text{ radians} \end{gathered}[/tex]
therefore, the answer is
[tex](10.05\text{, 3.04 \rparen}[/tex]
I hope this helps you
