Solve 3 sin(2t)+3sin(t)=0 for all solutions 0≤t<2π

Question

Solve  for all solutions 

 = 

  Give your answers accurate to at least 2 decimal places, as a list separated by commas

Answer 1

You need to use the double angle identity to rewrite sin(2t) in the equation as 2sintcost:

3(2sintcost)+3sint = 0

Now you can factor out the sint:

sint(6cost+3)=0

Use the zero product property:

sint=0 and cost=-1/2

solve each individually on the interval [0, 2pi)

sint=0 when x = 0, pi (using the unit circle y-coordinates)

cost = -1/2 when x = 2pi/3, 4pi/3 (using reference angle pi/3 in Q2 and Q3 where cosine is negative)

Four answers: x = 0, 2pi/3, pi, 4pi/3