Pythagorean Properties for Trigonometry

This page has a bunch of trigonometric properties.

This site derives the different pythagorean properties.
Here is trig property matching site.

Its SNOWING...

I stumbled upon this blog. I thought it was interesting. It looks like this class is doing pretty much the samething we are doing. Notice this post about the Pythagorean Property. I also like the idea of having students as scribes to blog about what happened in class each day. I am definately going to think about incorporating that into the class.

Here is another math blog. A. B.

Polar Coordinates

Here is an example of polar graph paper. Notice that its circles of different sizes.

What would the polar coordinates be for the point indicated on this graph?


I would estimate (4, 48 degrees).

Here is the wikipedia entry for polar coordinates.

This website might help. Here is another.

Here is a java script that is pretty good.

NO.NO.NO.NO.

The Physics teachers (thanks Mr. Lin and Ms. Kovacs) said that we are not done with HighDive. They said that it's okay to neglect the wind resistance, to neglect the "mass" of the diver, to neglect the friction in the bearing of the Ferris wheel, to neglect the fact that we would need Hulk Hogan to hold the diver by his legs, and to neglect the unlikeliness of a diver being able to actually dive into the cart and not SMASH his face on the bottom of it.

BUT, there were adamantly against us not taking the initial velocity of the diver into account.

What do they mean by the "initial velocity" of the diver?

Quiz

Friday we will have a quiz that will address Goals 1 and 2.

1. Graph trigonometric functions and variations on those functions (and be able to identify the critical points)


2. Relate the concept of inverse functions to define inverse trigonometric functions (and be able to find missing angles)

How comfortable are you in regards to these 2 goals?

This is a pretty good study guide. Here is another one.

Here is a good site to see how changing values affects the amplitude, period, and the midline.

What is a sine equation that represents this graph?

Cool Physics Pics

These are some cool pictures. But, do they relate at all to our High Dive Unit problem?

Almost Done?

I think we have learned enough to solve the unit problem.

We have equations to calculate the height of the diver, the x-coordinate of the diver, the fall time of the diver, and the x-coordinate of the cart.

We tried to see if the diver would fall into the cart if the wheel time (W) was 13.33, and we discovered that the cart would pass the diver.

On our group quiz, we tried to see if a wheel time (W) of 9.5 would work, and from examining the quizzes, most groups are saying that "NO" the diver will not fall into the cart.

What strategies could we use to solve for the "right" W?

Equations...

Today in class we generated several equations.


Which ones were helpful? Which ones should we definately have in our notebooks? Which ones should be taped to the wall of our classroom?

One equation we discovered was for fall time -- and I don't mean autumn. Can you use your calculator to calculate the correct fall time if I give you a "wheel time" of 22 seconds?

Ferris wheel videos

Not me...


Interesting...


Can we rent this for Fun Fair?


This looks amazing, but I would have to close my eyes...


We should bring this guy to Navy Pier with us...

FreeFall

Answers are posted on the Homework Site.

It looks like the mass of an object doesn't affect the time it takes that object to free fall. Does that make sense? A grape and a bowling ball dropped from the same height will take the same amount of time to fall to the ground?

Any questions, comments, or suggestions?

Check out this video.

HW8

What was the point of HW8?

Isn't average speed just the average (mean) of the inital speed and the final speed?

What's the average speed of this graph (from 0 secs to 20 secs)?

HW7 Part 2

How do we solve these problems from HW7 Part 2?

• How do we find 3 values of θ, other than 15°, such that sin θ = sin 15°?
• How do we find 3 values of θ, such that sin θ = -(sin 60°)?
• How do we find 3 values of θ, such that sin θ = 0.5?
• How do we find 3 values of θ, such that sin θ = -0.71?

What strategies can we use?

Check this link out. Here is the beginning of the unit.


Here is a quiz to test your understanding.