the easiest way to use sum and difference trig formulas for big angles

In this math example, we are trying to use a sum or difference trig formula to calculate the exact value for a larger degree angle. We want to use 30, 45, or 60 degrees to do this calculation because these are known ratios. Because of this larger angle that we are given, no two pairs of those angles add together to our given angle. Therefore, we want to find a reference angle. This means placing the given angle into the correct quadrant, drawing in our reference angle (always to the x-axis), and calculating the reference angle by subtracing the smaller angle from the larger that make up the reference angle. When we replace the original angle with the reference angle, we also must check to see the overall sign (positive/negative) of the function. I like to use the phrase "All Students Take Calculus" to remember in which quadrant each function is positive. This leads us to include a negative in front of our function that carries along when we fill into the difference formula for cosine. For this example, we go through the two different options that we had that subtracted to make 15 degrees. The angles that are filled in for each piece of our formula are color coded to help see where they were filled in. After using the difference formula, we evaluate each of the known trig functions to give us nice exact ratios. The solution is then reduced fully to give the best solution possible.
cos(165)
This video contains examples that are from Algebra and Trigonometry, 1st ed, by Abramson, Belloit, Falduto, Gross, Lippman et al. It is an open-source textbook from OpenStax that you may download for
free at openstax.org/d.... The text is licensed under the Creative Commons Attribution license. creativecommon...