Question

Question #5b8a3

Answer 1

`(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)`