Question

Precalc, please help?

Find the distance between the points with polar coordinates (3, 120°) and (0.5, 49°).

I got 2.035, but I am not sure if that is right.

Answer 1

x=cos theta
y=rsin theta.
\[x1=r \cos \theta =3\cos 120=3\cos \left( 180-60 \right)=-3\cos 60=\frac{ -3 }{ 2 }\]
\[y1=rsin \theta=3\sin 120=3\sin \left( 180-60 \right)=3\sin 60=3*\frac{ \sqrt{3} }{ 2 },\]
similarly find x2,y2
then
\[d=\sqrt{\left( x2-x1 \right)^2+\left( y2-y1 \right)^2}\]