What Could Have Been A Snowday...

Mr. O'Brien's back!!

To start class today we tried to graph BY HAND on graph paper these two equations:
a) where the period is π and the amplitude is 1


















b) where the period is 8 and the amplitude is 1















If you are having trouble with graphing, feel free to use the applet http://hotmath.com/util/hm_flash_movie_full.html?movie=/learning_activities/interactivities/translating_scaling.swf. You can also use your TI, Grapher, or Geogebra to check your own work. Personally I really like Geogebra because it's easy to interpret. On quizzes, you'll want to be able to use your TI to help you. Remember to scale the TI graphs by using the "ZTrig" zoom option.

These would be good practice to do if you were absent. The next homework quiz will be on Wednesday, so if you've been having trouble with graphing trignometric functions, tonight and tomorrow night would be a great time to do that.

Remember that for every graph you do in this unit, you'll need to have 5 Key Points. The starting point of sin(x) is (0,0) - for cos(x) it is (0,1). Divide every wave into four equal parts (use π to scale the x-axis if that's more convenient). The starting point and the four points you just made are the 5 Key Points - using these gives you one full period of the graph

The function cos(x) has y-axis symmetry (even) & the function sin(x) has origin symmetry (odd).

The equation to find period change for transformations is . Remember that the equation for any trigonometric function is . You need to know what each of those variables mean and how changes in those variables affect a graph. A good way to change your equation a bit is to factor out the b from the x and h so that you're left with an equation that's easier to understand. This helped us a lot on a).

We discovered a cool identity: . You don't need to know it, but we learned this from playing around with symmetry. Keep symmetry in mind as we look at how graphs relate to each other.

After discussing the warm-up we went over last class' quiz. If you are having trouble with these problems take that as a warning that you probably need to come in for extra help. Don't worry too much if you're having a hard time, but keep working on the things that you're having trouble with. Mr. O'B tries to give partial credit when he can. 15/30 means you're on the right track!
Key Ideas From This Quiz:
* for #3 - to undo a sin you have to do the function on your calculator
* stay in radian mode on your TI!!
* for #5 - Use Pythagorean Theorem
* for #7 - remember to put in the first quadrant in order for both angles to be in SP
* #10 - if you want to get the secant from the tangent just remember that cosine is negative, so secant will also be negative (you're in QIII). Make a right triangle to help you find the other sides

Next we looked at the parent functions we drew last class for notes. If you need to find the graphs for any of the 6 functions you can look on the back cover of the textbook. Also, Nick's last blog post included the graphs of tangent, cotangent, secant, and cosecant. We examined these four graphs very closely and began to understand how they work a little better.
* Tangent & Cotangent: odd. Period = π
* Secant & Cosecant: even.

You don't really need to know the parent function for cosecant - all you have to do is know what sin looks like. To see why this is, you can graph both on one graph and that will illustrate this property to you. Shortcuts are always nice.

If doing trigonometry homework makes you want to cry, check out http://oakroadsystems.com/twt/.

ATTENTION: NEXT CLASS WE WILL BE HAVING CLASS 3A & 3C. EAT LUNCH DURING 3B. Mr. O'Brien will email everyone to remind you. He has ski stuff going on that day. Grazie ragazzi.

Sorry for the long post! Next scribe will be everyone's favorite ginger kid, Lange King (sorry Julia). Homework is on the iCal. Keep asking questions!