At this point students know all of the trig identities and have been using them to solve equations and figure out trig values at specific angles. Today is a chance to take a breather and to really reflect on all of these properties.
The first activity for today involves index cards, masking tape, and lots of movement and talking. Students will be given an index card that has the formula for a trig identity on it. Without looking at it, students will tape it to their forehead and will try to figure out what their expression is equivalent to.
Teacher note: make sure you test different kinds of tape - I find that masking tape works well and doesn't fall off easily.
The catch is that they can only ask "yes" or "no" questions to their classmates. Students will be able to walk around and ask one question from each student. Once they figure out what identity they have, they can come up to the front of the room and you will check it on the answer key that you have. If they get it correct, I give them the worksheet that we are doing today (attached in the next section).
I find that it usually helps to model this game for my students to get them thinking about good questions to ask. I always start by taping one to my forehead and asking students about it. Some example questions are given below.
This worksheet is a good summary of many of the concepts that we have worked on in this unit. As we are nearing the end of the unit, this is a good opportunity to focus on the big picture and to think about how these relationships work.
On the first page of the worksheet, students have to simplify the expression using one of the identities that they know. For example, #1 would become sin(99°) once simplified completely. I usually go through this one as an example to let students know that they may need to use two formulas (the cofunction identity and the sum formula in this case).
The last question instructs students to find the exact value of sin(18°). This is a challenging problem but it walks them through the process. It is a worthwhile problem because is combines so many different facets (trig identities, factoring, solving for a variable, polynomial division, and possible sine values). My students struggled to get started, but once they got through the first few steps they were on their way. It definitely helps to have them working in groups to bounce ideas off of each other.