# Monday 4 December and Wednesday 6 December classes

(Wednesday after Test 4)

Topics:

• Filling out the unit circle important points in the first quadrant (for use in solving trig equations today)

You can practice this using a copy of the handout:  Unit circle for practice. You should be able to fill out all the important values along with their angles in less than 5 minutes. It is also useful to put the values of tangent for each of the important angles outside the circle (near the point on the circle).

• Solving the basic trig equations $\tan(x) = c$, $\cos(x) = c$, $\sin(x) = c$, (continued): see the summary on p. 277

• Solving more complicated trig equations by breaking them down into one or more of the basic trig equations.

We discussed Examples 20.11(a) and 20.12(a,b), as well as the solution to Exercise 20.4(h)

• Vectors: finding the magnitude and direction angle.

The handout I gave out in class is here: MAT1375VectorsMagnitudeDirectionAngle

We worked through all but the last two examples. You will finish those for homework. (They are also done in the textbook.)

Always make sure that you draw the vector in the coordinate plane before doing anything else. Sometimes it is obvious what the magnitude or the direction angle is without doing any computations! And you always need to know which quadrant your vector lies in (or along which axis).

Homework:

• Review the examples discussed in class and make sure that you understand how we are proceeding!

• Practice filling out the unit circle from memory and check your results. You need to be able to do this very quickly and accurately.

• There is no good WeBWorK for these topics, alas. So you will do the following problems from the textbook, and I would like to see some of them on the board next time:

Exercise 20.4(all parts, but especially f, g, i, and k)

Exercise 22.2(a-1): also finish the last two examples on the handout

• Also I would like to see some of Exercise 17.6(a-k) (previously assigned, sine and cosine graphs) on the board, with explanations of how you found the five important points. Please see my new post which includes an improved version of my notes and a video (slideshow with audio) giving two worked-out examples.

• Please take a look at the Final Exam Review sheet which is here

I am breaking the review into two parts. For Monday please prepare the following problems: #4, 8, 9. I will ask for volunteers for at least some parts of these.

Review links related to problem 4: please read or view these even if you think you don’t need to!

Difference quotients from PatrickJMT: Example 1 Example 2

For #8, see the review self-tests for Test 4 and Example 14.3 in the textbook – make sure that you are using the properties of logarithms!

For #9, see this post

• My plan for next class new topics is to do polar form of complex numbers. You may wish to view these videos from PatrickJMT to see a bit of where we are going:

What we are doing is basically looking at complex numbers as vectors in the plane!

Don’t forget, if you get stuck on a problem, you can post a question on Piazza. Make sure to give your question a good subject line and tell us the problem itself – we need this information in order to answer your question. And please only put one problem per posted question!

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