Week 9: Using trig identities to solve trig equations

This is the week before test 2, so the session could be about preparation in terms of getting homework and other questions answered.

We'll also use trig functions and their inverses and their domains and ranges, along with trig identities, to solve trig equations.

This handout provides students with the trig identities they'll need to know, along with 10 practice problems. We'll solve these problems in ways that draw on the relevant concepts in order for a richer, broader exam prep experience.

Week 8: Sinusoidal functions (cont.) plus...

Meetings were cancelled for three of the five groups last week, so we'll complete the activities with groups who haven't done so.

Then we'll try this problem. It's about developing a sinusoidal function to match a given graph. The answer is in the first comment below.

There were also 2 problems from the text that we didn't get to from Week 7, which should be suitable for some good, productive groupwork. Let's see how those work out.

Expect a 10-minute warm-up of questions to be solved using the unit circle.

Week 7: Exploring sinusoidal functions

Well, we didn't spend enough time on the activity in week 6. There was homework to do, and my plans for networking and groupworking didn't come to pass.

This week, we'll explore transformations of the sine and cosine functions to parallel section 6.5 in the book and revisit transformations of functions in general. At the same time, we can hit those big words we didn't quite get to last week. I'm especially thinking about: period, amplitude, midline, horizontal shift, and phase shift.

We'll develop procedures for finding these values when given sine and cosine functions in a variety of forms, and vice versa. Then we'll apply the procedures to develop models of realistic situations. Textbook problems 28 and 35 (section 6.5, p. 277) are fine candidates. Download them here.

Week 6: Exploring the trig functions

Last week, we developed our understanding of the sine and cosine functions by connecting their graphical, numerical, and geometric representations. This week we explore those functions and the trig function that composes them. We'll assemble a network-of-sorts using the graphing calculators and use that network to structure the mathematical activity using students' contributions. We move back and forth between big ideas and their instances. And we use big words like periodic, amplitude, midline, symmetry, transformation, phase shift, inverse, domain and range, global max and min, roots/zeros, and arc length.

This link takes you to a collection of trig-related applets, some of which we'll use in class to explore these functions.

Wolfram|Alpha is also a handy tool for exploring functions and other mathematical objects.

Students who haven't completed the activity from week 5 should do so before heading on to this exploration.

[Nothing to download this time.]