How do you find all the solutions inside an interval?

06:57 mins, "How do you find all the solutions inside an interval?" Transcript

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Oftentimes in a trig class you'll be given a trig equation like the one in this video and asked to find the solutions of the equation inside a particular interval.

The easiest way to solve a problem like this one is to first put the entire equation in terms of sine and cosine, instead of any of the other circular trig functions. Then you'll want to move all of the terms to one side of the equation, such that the other side is now equal to 0.

Then, hopefully, you'll be able to apply zero theorem to solve for the values of the angle theta that make the equation true. Once you've done that, you'll want to compare those values to the interval you've been given, and you'll ignore any solutions that are outside the interval. For your final answer, you'll list only the solutions you found that are inside the interval. You need to make sure that you consider whether the interval includes one or both endpoints, or if the endpoints are excluded. You'll want to list a solution that falls on an included endpoint, but ignore a solution that falls on an excluded endpoint.

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