Question #5b8a3

1 Answer
Dec 11, 2016

#(r, theta)=(3.1623, -18.435^o)#

Explanation:

The conversion formula #(x, y)=r(cos theta, sin theta)#.

Here, #x = r cos theta=-1 and y = r sin theta = 3#

So,

#r =sqrt(x^2+y^2)=sqrt10=3.1623#, nearly,

#cos theta = x/r=-1/sqrt10 and sin theta =3/sqrt10#.

The prefixing signs # - +# reveal that #theta inQ_4#.

The calcular value #sin^(-1/sqrt10)=-18.435^o in Q_4#

So, #(r, theta)=(3.1623, -18.435^o)#.

Note: Had you used the cosine value, the calculator display will be

+18.435. But cos(-theta)=cos(theta) and we can change the sign for

the shift to #Q_4#, wherein sine is negative. If you require

a positive equivalent of #theta#, for the same direction,

it is #(360-18.435)=341.565#, the coordinates become

#(3.1623, 341.565^o)#