Question

what is the simplest form of sin3theta? i broke it down to 3sintheta-4sin^3 theta but i got stuck at trying to break down the sin^3 theta...

Answer 1

\[\sin3 \theta=3\sin \theta-4\sin^3\theta=> 4\sin^3\theta=3\sin \theta -\sin 3\theta\]\[\sin^3\theta=\frac{3\sin \theta-\sin 3\theta}{4}\]

Answer 2

hmm... this is making me confused.. because i'm going back in circles. i'm trying to convert the polar equation r=sin3theta to a rectangular equation but i always return to r^2=2r(-sin3theta) for some reason...

Answer 3

put the problem...exactly..its not clear to me..

Answer 4

convert the polar eqn to rectangular form. r=2sin3theta

Answer 5

r^4=2r^3sin3theta
\[r^4=2r^3 (3\sin \theta-\sin^3 \theta)\]
\[(r^2)^2=2r^2(3rsin \theta)-2(rsin \theta)^3\]
\[(x^2+y^2)^2=2(x^2+y^2)3x-2x^3\]

Answer 6

now solve it..

Answer 7

thanks!