Inverse Trig Functions: Formative Assessment
Lesson 11 of 14
Objective: SWBAT evaluate and graph inverse trig functions.
I will use today's Quick Quiz to getan idea of how students are doing with the inverse functions. If I see that students are struggling, I want to address specific problems tomorrow during the review of the unit.
I chose not to allow any calculators for this formative assessment. I want to know that students understand what an inverse is, and if they are just typing things in on their calculator, it will be difficult to know if they only have the procedural understand or if they have both procedural and conceptual understanding.
While students are working on the exam review, I quickly grade the Quick Quiz and intervene for students who did not get all of the questions correct. I call students up individually to discuss their quiz. If they got a question wrong, I ask them to explain their thinking. If a student got one or two wrong for question 1, it might not be a conceptual error. I plan to pay particular attention to Questions 2 and 3 and talk about those if a student did not get them correct.
For Question 2, I ask students which value is the angle measure and which value is the trig ratio. I stress that the trig ratios for tangent and cotangent, for example, are reciprocals - not the angle measures! Thus, if m is the angle measure in the equation, you should not take the reciprocal of it. It would not make sense to say cos(120°) = sec(1/120°). More on this in the video below.
If a student got Question 3 incorrect, I have them remind me about how and why the domain of the cosine function is restricted to make an inverse. A lot of times if students can sketch the original cosine graph, they can easily find the domain and range of the piece of the function that passed the horizontal line test and then switch them to find the domain and range of the inverse. Then, they can use the new domain and range to sketch the graph.