 In general, we can solve an equation involving a trigonometric function by rewriting it as trig function of theta equals c, where c is a number, finding a value theta that solves the equation, and using the periodicity of the trigonometric function to find other solutions. For example, suppose we want to solve two sine of 3x plus pi equals one, let's find all solutions, and then let's also find the least positive solution. So remember, to solve a trigonometric equation, it must be in the form trigonometric function of theta equals c, where c is a number. So we'll rewrite our equation. Now it's helpful to ignore the input. So even though we're trying to solve sine of 3x plus pi equals one-half, it's really sine of t equals one-half. And so the question is sine of what is equal to one-half? And we know that must be pi-six, and don't forget, sine is periodic if sine of theta is equal to c, then sine of theta plus 2pi is equal to c as well, and in fact, if we add any multiple of 2pi, we get another solution. Now put things back where you found them, was 3x plus pi, and so we have our equation, and we solve. So now if we pick an integer value of k, we can get a solution. Now in order for there to be a positive solution, k must be greater than zero, and so we find the least positive solution will be of k is equal to one, and so the least positive solution is x equals 7pi eighteenths. Or is it? And the thing to remember is that for most values c, sine of theta equals c has two solutions in the interval between zero and 2pi. So again, if we want sine of t equal one-half, we could also have t equal to 5pi-six. And again, plus any multiple of 2pi. And putting things back where we found them, we can solve for x and find, which gives us a second set of solutions. And for these solutions, the least positive solution will be where k is equal to one. And so we find, and our other solution, 7pi eighteenths, is actually the least positive solution, and so we'll go with it. Similarly if we want to find the least positive solution of cosine x-halves plus pi, one set of solutions to cosine equal to zero is equal to pi-halves plus 2pi-k. So our argument will be equal to pi-halves plus 2pi-k. And so x will be, and the least positive solution of this type is where k is equal to one, and so the least positive solution will be 3pi. But remember, there's another set of solutions. So another set of solutions to cosine equal to zero is equal to 3pi-halves plus any multiple of 2pi, and so we find that the least positive solution of this type is going to be where k is equal to zero, and so the least positive solution overall is x equal to pi.