The goal of this section is ensure that the students know how to find less common trig ratios using a calculator. My students did this the previous year but it is important to make sure all of the students are on the same page before we get into modeling with trigonometry.

I introduce the first non-standard angle and have the students locate it on the unit circle. I ask for ideas how we should go about finding the cosine of this angle giving them a chance to talk about it in pairs (Math Practice 2). I don’t tell them in advance that they will need calculators. I manage the conversation, potentially asking leading questions; until the fact comes up that we don’t have enough information or skill. This is where I introduce the calculator.

The next goal is to introduce (remind) students how to change between radians and degrees on the calculator. Once they have had a short tutorial, the rest of these problems should be speedy.

Now I ask the students to find an angle given the sine, cosine or tangent. Again, I give the students time to talk about the first problem. My students saw this in Geometry last year. During the discussion, hopefully someone brings up the arc sine. They have done many inverse operations, in fact, the last unit focused on logarithms which is the inverse operation of an exponential. This is a good angle to take in introducing the arcsine. The other important thing to focus on is what the arcsine is actually asking. For example, in the first problem, it would be asking us “what angle has a sine of 0.7563”.

Now, we talk about the fact that these trig ratios are true for an infinite number of angles so we need to place a limit. I start with 0 to 2π. There will be two angles for each problem. This is a great review of the location of angles with the same trig ratio(s).