Sine Law


It is used when you are solving
a triangle that is not a right triangle


a/sinA = b/sinB = c/sinC


this is the equation we must follow
in Sine Law.

for example:

A triangle has 2 angles and a side,
angleA = 30° and angleB = 65°
side a = 5cm, look for side b.

5cm/sin30° = b/sin65°

b = 5cm/sin30°(sin65°)

b = 9.06cm

sinA/a = sinB/b = sinC/c
this equation is used when 2 sides is given
and you are looking for the angle.

for example:

A triangle has 2 sides and an angle,
side x = 6.8cm
side y = 5.1cm
and angleX = 49°
find angleY.

sinY/5.1cm = sin49°/6.8cm

sinY = sin49°/6.8cm(5.1cm)

angle­­Y = 34.47°

this is how to use the Sine Law.

the next scribe is >> Iana <<

{}(-,-){} zzZ...

next scribe is Erick! ^^

Trigonometry-Functions of Obtuse Angles

TRIGONOMETRY





Labelling Triangles


- Use CAPITAL LETTERS for the angles.
- Use small letters for the sides.




Pythagorus Theorom


A² + B² = C²



Sin A = opposite/hypotenues : SOH


Cos A = adjacent/hypotenues : CAH


Tan A = opposite/adjacent : TOA



* adjacent is the side of the triangle, thats beside the opposite of the angle.

Example 1

EXAMPLE 2

FOR HOMEWORK

- do Exercise 17 , # 1-6 , 12-20

THE NEXT SCRIBE IS..

Haishan (:

Reflection

Wow. I didn't know we had to do a relfection. Well just finished doing the test. I think that I did okay. I thought this unit, was a bit hard since there was different formulas to use. As well which points to use. I hope the next unit isn't hard. Hope everyone did well on their test.

-->>reflection<<--

wha..i d0n't kn0w we need 2 d0 s0me reflecton..anyways here it is.. analytic geometry f0r me was like..graphing all d way..i h0pe we'll have d simpler one next unit..this unit kinda makes me c0nfuse like every less0n we were d0ing..s0 yeah..i still h0pw we'll have d simpler one..and i h0pe i did go0d in d test..cuz i guess it's n0t..so0 yeah..go0d luck next unit..

Reflection

I understand analytic geometry quite well, but I get confused easily. Especially the way the wordings are arranged. The formulas sometimes confuse me, but for the most part, I understand it. The test was okay, but there were some questions I did not get. Hopefully I did good.

reflection :

Mmmmm..... Our test isn't that hard but Im not quite sure if some of my answers are correct... I don't know...... I'm very busy this week and I forgot to post a blog / reflection for this test.... OMG!!! I lose points for not doing this blog.... well, that's OK at least I have one now... heh... heh... heh...

I guess I'm very lucky this day. Our teacher gave us permission to use our formula sheet and it's very useful... whenever I forgot about something, I just look at the formula sheet and I remember all the things that I forgot!!!! kinda weird........ but that's the way it is !!!..... hope I did well on this test and let's wait for the results....... GOOD LUCK !!!

This unit was kinda hard for me because of "problems" lol. The formulas are kinda easy but I have this short term memory thing going on so I forget stuff. The test mi ght be hard for me this time around cause I have to study for "Filipino Language Exam" (yeah... study).... Kinda sad.... Good luck to the people taking the exam and good luck! Hope you guys get a good mark... (inside intent)

Reflection

For this unit i thought it was quite straight forward. i had some problems using table of values but then i got used to it. Some things that i thought was easy was the y-intercept. And yeah thats about it.. haha good luck on the test guys

Analytic Geometry Reflection

This unit wasn't that difficult for me --- I did have a lot of catching up to do after I missed a week while I was out of town, however. I'd say the hardest part was probably figuring out which formula to use when. I'm going to study a lot tonight. I'm very anxious, but hopefully I'll be able to pass the unit test tomorrow! =D

reflection

just got home, haven't study for my test yet. but i hope that i can pass the test though. but actually i dont think that i can pass the test, cuz graphing is so hard for me. and sometime i got mess up with the formulas. gud luck to everyone! have to study now. ^^

Reflection:

This unit was like the same in my last unit. Easy to understand, although, in this unit I need to watch my math more carefully so I dont lose any easy mistakes. Good luck to everyone :)

Cheers,
Jenn (:

Reflection

k, I don't know if we were supposed to make a reflection but I'm making one anyways.

This unit was okay, it wasn't super easy but it wasn't super hard. I learned a lot of new things, and at times I felt kind of confused with the questions, because I wasn't sure what they wanted me to do. But now that I finally reviewed my notes and stuff today things finally click! But it's pretty sad.. But anyways I feel slightly comfortable with the stuff now.

:):):):):):):):):):):):)

OMG this math test is gonna be hard!!! LOL ...i think well for me it will since i forget easily hopefully i will study my butt off till i remember but cheeaa i will study forshure no lies the excersizes for me are quite challenging but i like challenges as long as i have my notes right there i'm good! well good luck to all in the test and allans cool!-__-

reflection.

For this unit. I pretty much got through it alright. But then, since there are lots of equations to remember, i always get them mixed up. So hopefully, I do well on the test.

~Reflection~

Oh maaaaan. I almost forgot about this? We're we even supposed to do this? =S haah. Well okay then here it is:

This unit was okay? I mean like it wasn't hard but it wasn't easy either. There's quite a few formulas to remember so I guess that makes it kinda hard. The easiest part was probably figuring out the x and y intercepts and graphing the line. The hardest part was probably finding the equation for the perpendicular line? I used so much graph paper in this unit! But, oh well... K so anyways, yea I think I'll do okay on the test yenno as long as I don't mess up on the formulas and getthem mixed up or something? So yea, I guess that's all! Good luck everyone!

~pj~

October 18th, 2007

Graph the following equations onto one sheet of graphing paper:
y = 2x + 1
y = 2x + 7
y = 2x - 3
y = 2x - 7

This is what it should look like:
(click to view it much better)


Note that..

• all these lines are parallel
• lines that are parallel have equal slopes

Parallel lines

• never touch each other
• remains the same distance away to infinity
• equal lines

Perpendicular lines

• cross forming a 90° angle
• the slopes of the two lines will be negative reciprocals

If the slope of the perpendicular is a result of a negative reciprocal then it should look like this :
m = 2/1
m"perpendicular" = -1/2


Find the equation of the line to y = 3x + 4 that goes through (7, 16).

m = 3/1
point: (7, 16)

y - y1 = m(x - x1)
y - 16 = 3/1(x - 21)
1[y - 16 = 3/1(x-21)]
y - 16 = 3x -21
y = 3x - 5

Standard Form : 0 = 3x - y - 5

Easy right? Time to use m "perpendicular":


Find the equation for the line "perpendicular" to y = 3x + 4 that goes through (7, 16)

m = 3/1
m "perpendicular" = -1/3

y - y1 = m (x - x1)
y - 16 = -1/3 (x - 7)
3[ y - 16 = -1/3 (x -7) ]
3y - 48 = x + 7

Standard Form: 0 = x + y -55


Homework: Exercise 16: Determining Equations of Lines - 3
Questions 1- 15

Test moved to Tuesday, October 23, 2007
Next scribe is KARENd, heres my other present for you c(:
Her birthday was yesterday everyone, for anyone who didnt know! :P


Cheers,
Jenn (:

October 16

Finding Equations

1.) Use Slope Intercept

y = mx + b

m = slope
b = why intercept

2.) Point-Slope form

y - y1 = m ( x - x1)

m = 3 P(7, 36)

y - 36 = 3 (x - 7)
y - 36 = 3x - 21
y = 3x - 21 + 36
y = 3x + 15 ---> slope intercept form ( y = mx + b)

Ax + By + C = 0 ---> standard form
3x - y + 15 = 0 ---> (Ax always have to be positive)



Example:

D(6, 1) E (-4, -3)
D(x1, y1) E (x2, y2)

1.) Find the slope

Y2 - Y1
_____
m =
X2 - X1


(-3) - (1)
______
m =
(-4) - (6)


m = -4/-10

m = 2/5

2.) Use point-slope form

y - y1 = m (x - x1)
y - (-3) = 2/5 [x - (-4)]
5 (y + 3) = [2/5 (x + 4)] 5
5y + 15 = 2x + 8

Ax + By + C = 0

2x - 5y - 7 = 0

P(13, -15) m = -7/2

y - y1 = m ( x - x1)

y - (-15) = -7/2 (x - 13)
2(y + 15) = [-7/2 (x - 13)]2
2y + 30 = -7x + 91

Ax + By + C = 0 (standard form)
7x + 2y - 61 = 0

Do exercise 15, 1 - 12

Sorry if this is posted a day late. I had some difficulties with my interent.
next post is jlavina

own opinion

oh my god, i hate graphing... i always get confuse with that.

Today's Lesson 10/15/07

We learned about: Equation of a straight line.
Today's notes:

1. y=mx+b --> m=slope, b=y-intercept
2. Ax+By+C=0 --> Standard form (in general set up so "A" is positive)
3. Ax+By=C


Examples:


m=3 b=2

y=mx+b
y=3x+2


m=-4 b=5

y=mx+b
y=4x+5


Assignment: Ex 13 - All questions but don't do # 13, 14 and 17

Next scribe is: preyes

today's lesson 10/10/07

We learned about.. Graphing lines using slopes.
Todays notes:

the equation is set up as y=mx+b
^ ^
m = slope intercept = b

1. Put the equation into y=mx+b
2. Plot the y intercept
3. Use the slop to find a 2nd point
4. Draw a line

eg. -2x+y=-3
y = 2x-3
y =2(0)-3
y=-3


Then plot it out on the graph.
and we received exercise 12, questions 1-9 + 11-15

Oh by the way, look at the comments to see who the next scribe is Laura.

Graph Using Intercepts

Notes for today's class....

Graph using intercepts
-needs 2 intercepts

Those 2 intercept are:
1) x- intercept
- the place where the line crosses the " x " axis
y= 0

2) y- intercept
- the place where the line crosses the " y " axis
x= 0

Ex. 1
2x+3y=6

x=0
a) 2x+3(0)=6
2x=6 (divide both side by 2)
x=3

y=0
b) 2(0)+3y=6
3y=6 (divide both side by 3)
y=2

after you solve those 2 intercepts you have to graph it...

(Sorry if I can't make the graph I don't know how to make a graph line here)

Ex.2
2/3x + 6y= 12

x= 0
a) 2/3x+6(0)=12
2/3x=12 (multiply by 3, both side)
x=36/2
x= 18

y= 0
b) 2/3(0)+6y=12
6y=12 (divide both side by 6)
y=2

after yolve graph those 2...

Ex.3
3x-5y=-15

x=0
a) 3x-5(0)=-15
3x=-15 (divide both side by 3)
x=-5

y=0
b) 3(0)-5y=-15
-5y=-15 (divide both side by -5)
y=3


(graph those 2)

assignment
Ex. 11 questions 1-9, 11-16

enjoy!!!!!!! :)
next scribe is... teara :)

GRAPHING LINES

A line can be represented by an equation in different ways:

1. Ax + By + C = 0
2. Ax + By = C
3. y = mx + b

Three Ways on how to graph an equation:
a. Table of values

x -1 0 1
y 3 1 -1


Solved for this equation: y=-2x+1
Just simply substitute the x variable above

If x = -1
y=-2(-1)+1
y=2+1
y=3


if x=0
y=-2(0)+1
y=0+1
y=1


if x =1
y=-2(1)+1
y=-2+1
y=-1


So (-1,3) (0,1)(1,-1) plot them in your graphing paper....,,


answer exercise #6 1-12,16-20 :>


raminalyn...............hi!!!!!!!!!!

Yesterday we have a new topic.....It's about slopes...It's not tricky butit's fun learning new stuff...Got two finish exersice no.7 the tricky part was no.3and 4....,have a nice long weekend and thank you for the greetings...
the next one that will subscribe is kim...,

Polynomial Test Results

Hello folks.
I finished marking the tests, and would like to let you all know that the class average on this test was 64%. Pretty good for the first pre-calculus test.
Congratulations to all on the test.

Mrs. Ingram

Reflection, again:

I dont know where my old one went -_-'' For some reason its not on here, but as i said before this unit was a easy to understand, although im pretty careless and then i have to do extra work by doing check on a few questions. Um, next unit seems more familiar to me than this one, so i may have better luck (y)! Good luck for everyone next unit!

Cheers,
Jenn (: