Question

Convert the point from Cartesian to polar coordinates. Write your answer in radians. Round to the nearest hundredth.(-10, 1)

Answer 1

`(10.05\text{, 3.04 \rparen}`

Step-by-step 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

`\begin{gathered} r=√(x^2+y^2) \\ \theta=\tan^(-1)((y)/(x)) \end{gathered}`

Step 1

a) let

`\begin{gathered} (x,y)\Rightarrow(-10,1) \\ so \\ x=-10 \\ y=1 \end{gathered}`

now, replace in the formula

i) magnitude ( r)

`\begin{gathered} r=√(x^2+y^2) \\ replace \\ r=√((-10)^2+(1^2))=√(101) \\ r=10.05 \end{gathered}`

ii) angle

`\begin{gathered} \theta=\tg^(-1)((y)/(x)) \\ replace \\ \theta=\tan^(-1)((1)/(-10)) \\ \theta=-0.0999\text{ radians} \\ or \\ \theta=-0.0999\text{rad}\imaginaryI\text{ans+}\pi \\ \theta=3.04\text{ radians} \end{gathered}`

therefore, the answer is

`(10.05\text{, 3.04 \rparen}`

I hope this helps you