Fidn all the values of θ with θ_< θ< 2pi such that sin(3θ)= -0.5
Ok. You need to show the initiative on this forum. We'll help you get unstuck, but the rule is that people asking for help basically have to do the work. Otherwise, we're not helping you understand. So, show us some work, and we'll help you get unstuck.
It's a simple Trig equation and the problem wants you to find all the angles in that interval such that the equation holds for them. It can simply be solved and you don't need to graph it by calculator!!!
sin(3x)=-.5=sin(-pi/6) => 3x=2kpi-pi/6 and 3x=2kpi+pi-(-pi/6). => 3x=2kpi+7pi/6
since 0<=x<2pi => 0<=3x<6pi. Now we want to fint all the ks such that the last inequality holds. By getting k=0 and k=1, that holds! that is if k=0 => x=7pi/6 . if k=1 => x=11pi/6. The equation has another answers for those ks; but the red ones are the only acceptable solutions!
Note: you could calculate the solution sets for x and then find xs in the first interval; but may be a bit hard!