Here are some sample problems that you may choose to use for the assessment of this unit:
While these problems all may look straightforward, there are many, many layers to each problem as students must keep in mind a lot of the knowledge that we have learned throughout this unit and the previous one.
For question #5, I ask students why the plus or minus symbol is an essential part of the cosine half angle formula. I want them to understand that this formula is derived from the double angle formula and that since there is a squared term, when we take the square root of both sides we get plus or minus. Also, I want students to understand that the sign (plus or minus) of their answer when using the formula depends on the quadrant. For example, if x is 300 degrees and use the half angle formula, we get cosine of 150 degrees. Since 150 degrees is in quadrant II, the cosine value would be negative.