Slope, tangent, and introducing inverse trig functions

I read through the exit slips I had students produce last class. On each slip, I made comments or wrote questions to push student thinking further. At the start of class, I asked students to write on the board their solutions to the last three problems (15-17) on the Relationships with Meaning packet.

At this point I checked to make sure students had calculated the slopes in problems 12-14. There was some disagreement on the value of the slope in problem 14. Everyone had that the slope would be negative but values were slightly different: -1/2, -3/2, -5/4. I used this as an opportunity to discuss how work could be checked. Other than students saying to ask others, they didn't have any way to verify their work. I pointed out that they could check slope using multiple points. This allows students to verify their own calculations rather than relying on others.

We then turned our attention to problems 15-17. There were no questions on problem 15, the work on problem 16 had failed to square the value √116. A few students immediately recognized the issue and corrected the error. Problem 17 was done correctly. Overall, students seemed fairly comfortable with the work.

At this point, I passed back the exit slips to each student. I then labeled as angle A the angle opposite the "height" leg of each triangle that was drawn for problems 15-17. I asked students to calculate the tan(A) for each triangle. I then asked students to look at the calculated slope, the tan(A) and what they had wrote the previous class about connections between slope and trigonometric functions. I had the class capture their thinking and connections in their notes.

I next moved into Finding the Value of a Relationship investigation. I started by showing students how to use the trig table to find an angle when they are given the value of the trig ratio. I want students to work through inverse trig functions using a trig table first so they can better connect the back and forth nature of angles to trig ratios and back to angles. Once this connection is solidified, I will show them how to use a calculator to get a more precise result.

Students started working through the first 6 problems. Questions arose about having to find all of the sides lengths. I had to clarify that they only needed for the first problem to identify the trig ratios they could calculate for the given values.

I asked students to do their best to complete the first 6 problems for homework. We'll start next class be looking at how well they did on these problems.