 In this video, we provide the solution to question number 10 for practice exam number 3 for math 1060 in which case We're asked to find all the solutions to the equation cosine theta minus 2 sine theta cosine theta equals 0 We want to find these on the interval 0 to 2 pi So we're going to be solving this in radians When I look at this equation the first thing I notice is the right hand side is 0 So maybe I could factor the left hand side the left hand side There is a common divisor of cosine theta So factor that out this gives us cosine theta times 1 minus 2 sine theta is equal to 0 So we can set each factor equal to 0 you get cosine theta equals 0 and we get 1 minus 2 sine theta Equals 0 so solving these the first one's basically there cosine theta equals 0 When does cosine equals 0 that happens at the top of the unit circle in the bottom of the unit circle So we're going to end up with theta equals pi halves and 3 pi halves from that one We only have to find solutions up to 2 pi so I can I don't need anything else I don't need like a 2 plus 2 pi k or anything like that for the second one subtract 1 from both sides We get negative 2 sine theta equals negative 1 divide both sides by negative 2 we get sine theta is equal to 1 half When does code when does sine equal on half that'll happen in the first quadrant and in the second quadrant in The first quadrant that'll happen at pi 6th in the second quadrant that'll happen at the angle which references pi 6th Which of course is pi takeaway pi 6th in other words you get 5 pi 6th like so And so when we put all these solutions together we get the final answer We're going to get pi 6th pi halves 5 pi 6th and Then 3 pi 6th so there are 3 pi halves Excuse me. There are four solutions to this equation here