February 4, 2010

Class started off today with a homework quiz, which we had twenty minutes to do; it was based on the homework problems that we have had for the past couple of days.

Then we went over homework questions from last night: page 291, #'s 71-93 odd, 100-106, & 108. We had questions with 103, 93, 75, & 73b.

Question 103 had to do with angular and linear speed. The formula for angular speed is , & the formula for linear speed is . Question 73 had to do with the minutes & seconds of already tiny degrees. Mr. O'Brien said to do it with this kind of format:

330˚ 25' = 330 + = 330 +

Which looks a little complicated, but actually makes sense. You basically just take the minutes & divide them by sixty to get the ratio (since there are sixty minutes in a degree), & then divide that by sixty again.

For 75, which was a little of the same but in a different order, you had to convert a degree with a decimal to a degree with its minutes. This one was 240.6˚, which we converted to 240˚ 36' by multiply the .6 decimal by 60 minutes; this gave us 36', which was the exact number we needed. Yay!

We moved on to the six trig functions next.. Which is kind of a big deal!



This is an example of a filled out trig circle, which will be referenced a lot in this post. Important symbols to know are:
r = radius
= radians
s = arc length

There's a quizlet on the blog that goes over the six functions of trig that you could find helpful. However, an easy way to remember these is SohCahToa.

y = a, r = c, x = b
Sin = y/r, Opposite over Hypotenuse, S-O/H
Cos = x/r, Adjacent over Hypotenuse, C-A/H
Tan = y/x, Opposite over Adjacent, T-O/A

Then we talked about the reciprocals of these equations.
Csc = r/y
Sec = r/x
Cot = x/y

As you can see, these angles are the inverses of their respective functions.

Then we went over the Japanese trig function applet, which allows you to input any degree for x, & it will output that angle in standard position, from which you can establish the sine of that degree. We did a little experimentation with the applet, & found out that in a UNIT CIRCLE (a circle whose radius is one):
Sin = y
Cos = x
Tan = sin/cos

CRAZY.

This means that:
Csc = 1/y
Sec = 1/x
Cot = x/y

Which was SO bizarre, because that meant that to find the cosine or sine of ANY unit circle, all you had to do was find the coordinates of the value & then choose either x or y for cosine & sine respectively.

EX: Find the sin45˚.
The coordinates on the unit circle for 45˚ is . So, since sin = y, the sin45˚ = . Which works!

You can do the same idea with the cosine, just use the x value of the coordinate rather than the y. A good site to help memorize the coordinates of these values (ew) is DudeFree.com, or the multitude of quizlets down below this post. I'm sure this is how everyone is going to spend SuperBowl Weekend, because this is so much more fun than anything else I can think of :D ... Just joking!! But seriously, this is a good idea to do at some point, even if it's just a half hour of studying.

Have a good weekend everyone! Anna, have fun scribing!