Reflection 24

Alright, so this week was another crazy with with no school on monday and a field trip thursday. Now I am completely lost in this class..ha. One thing I kind of understand now is 11-1.

I'll explain how to give the polar coordinates of something.
When do this you have to take the numbers it gives you and plug it into the formula r=+/- Square root of x^2+y^2.
Then plug in the coordinates again into theta=inverse of tan (y/x)
Type it into your calc. and then figure out what quadrant the number is in, and which ones you have to move to. Get your two numbers then put them into coordinates with the number you found by doing r=+/- Square root of x^2+y^2 (being your x)

Example:

Give the polar coordinates for (3,4)

r=+/- Square root of 3^2+4^2= +/- 5
Theta=tan inverse (4/3)
Quadrants 1 & 3: 53.130 & 233.130
Answer= (5, 53.130) (-5,233.130)

*This is converting rectangular to polar.

---------------------------------------
I'm pretty much confused about everything else in this chapter except for the stuff we learned friday. If someone could explain and give an example problem that would be nice :)

Reflection 23!

hm, so here's my second blog.

And after a 3 day week, and a 4 day weekends, i'm refreshed & rejuvenated & ready for another 4 day week! :)

Also, danceteam did awesome at State competition yesterday, can't wait for nationals in DISNEYWORLDDD! :)

to the math,
i'll finish off with the rest of the formulas:

Here are our half angle and double angle formulas

sin2a=2sinacosa

cos2a=cos^2a-sin^2a=1-2sin^2a=2cos^2a-1

tan2a=2tan∂/(1-tan^2a)

sina/2=±√((1-cosa)/2)

cosa/2=±√((1+cosa)/2)

tana/2=±√(1-cosa)/(1+cosa)=sin∂/(1+cosa)=(1-cosa)/sina

Ex:
Find the exact value of cos25 cos5-sin 25 sin5.

FIRST, You use the sum and difference formulas for sine and cosine.

SECOND, Add 25 + 5 when you look at the formula and that gives you sin 30.

THIRD, look at the trig chart sin 30 gives you 3/2 as your answer.

for half angles, i'll get it.
just need to look over it one more time, but if anyone could REfresh my memory, thanks! :)

Reflection 22!

So i definitely just noticed that i missed a blog & with danceteam competition all day, i forgot yesterday was Sunday so here it is...


for my first blog i'll explain the first half of our formulas:

Sum and Difference formulas for Cosine and Sine:

cos(A+-B) = cos A cos B -+ sin A sin B

sin(A+-B) = sin A cos B +- cos A sin B

Rewriting sum and difference as a product:
sin X + sin Y = 2sin (X+Y/2) cos(X-Y/2)

sin x - sin Y = 2cos(X+Y/2) sin(X-Y/2)

cos X + cos Y = 2cos(X+Y/2)cos(X-Y/2)

cos X- cos Y= -2sin(X+Y/2) sin(X-Y/2)

Sum formula for Tangent:

tan(A+B)= tan A+ tan B/ 1-tanAtanB

Difference formula for tangent:
tan(A-B) = tan A-tan B/ 1+tanAtanB


as for what i don't understand,
i'm still iffy with half angles but i'm sure i'll figure it out sooner or later. :)

thanks!

reflection make up

What is the trig chart you say?

well here it is.

0 = 0 degrees
pi/6 = 30 degrees
pi/4 = 45 degrees
pi/3 = 60 degrees
pi/2 = 90 degrees

sin 0 = 0
sin 30 = 1/2
sin 45 = square root of 2 over 2
sin 60 = square root of 3 over 2
sin 90 = 1
cos 0 = 1
cos 30 = square root of 3 over 2
cos 45 = square root of 2 over 2
cos 60 = 1/2
cos 90 = 0
tan 0 = 0
tan 30 = square root of 3 over 3
tan 45 = 1
tan 60 = square root of 3
tan 90 = undefined
cot 0 = undefined
cot 30 = square root of 3
cot 45 = 1
cot 60 = square root of 3 over 3
cot 90 = 0
sec 0 = 1
sec 30 = 2 square root of 3 over 3
sec 45 = square root of 2
sec 60 = 2
sec 90 = undefined
csc 0 = undefined
csc 30 = 2
csc 45 = square root of 2
csc 60 = 2 square root of 3 over 3
csc 90 = 1

Now, examples:
**a=alpha

4 sin pi/6 cos pi/6
=2 sin 2a
=2 sin 2(pi/6)
=2 sin(pi/3)
=2(square root of 3 over 3)
=square root of 3

cos^2 x/2 - sin^2 x/2
=cos 2a
=cos 2(x/2)
=cos x

I dont understand how to do the half and double angle problems either. those confuse me alot. it would be much appreciated if some one could help me out.

P.S. EDEE SCORED ON HOUMA CHRISTIAN TONIGHT WITH A BICYCLE!! AHHHHH!!!!!!!

reflection make up

Im gonna show yall all of the stuff you need to know:

cos(alpha+-beta)=cosalphacosbeta-+sinalphasinbeta sin(alpha+-beta)=sinalphacosbeta+-cosalphasinbeta

half angle and double angle formulas:sin2(alpha) = 2sin(alpha) cos(alpha)
cos2(alpha) = cos^2(alpha) - sin^2(alpha) = 1 - 2sin^2(alpha) = 2cos^2(alpha) - 1
tan2(alpha) = 2tan(alpha)/1 - tan^2(alpha)
sin(alpha)/2= + or - sq. root of (1-cos(alpha)/2)
cos(alpha)/2=+or- sq. root of (1 + cos(alpha)/2)

Rewriting a Sum or Difference as a Product:sin(x) + sin(y) = 2sin(x+y/2)cos(x-y/2)
sin(x) - sin(y) = 2cos(x+y/2)sin(x-y/2)cos(x) + cos(y) = 2cos(x+y/2)cos(x-y/2)
cos(x) - cos(y) = -2sin(x+y/2)sin(x-y/2)

sum and difference formulas for tangent:tan(∂+ß)=(tan∂+tanß)/(1-tan∂tanß)
tan(∂-ß)=(tan∂-tanß)/(1+tan∂tanß)

This is everything that you will need to know for your math test tomorrow. and the trig chart also. so study and i hope this helps you out because it all still confuses me.

reflection

Im gonna show y'all how to factor with trig functions. So yeah.

Factor.
2cos^2x - cosx - 3

The first thing that you do is that you take out all of the trig terms (sin,cos,and tan) and put a variable in there.
So you get

2x^2 - x - 3

now all you got to do is factor like a normal problem
(2x^2 -3x) + (2x - 3)
x (2x - 3) + (2x - 3)
x = -1 x = 3/2

Now plug that back in to your trig function
cosx = -1 cosx = 3/2

Now solve for the exact value
x = Pi and your other x is no solution because cosine cannot have a value of more than 1.

So when you get to the point where you need to factor trig functions just remember to break it down and replace the trig function with a variable, but after you factor don't forget to finish, like when you get cos = 1 don't leave it as that solve it all the way --- pi.

reflection

Sum Formula for Tangent
tan(alpha + beta) = tan alpha + tan beta/1-tan alpha (tan beta)

Difference Formula for Tangent:
tan(alpha - beta) = tan alpha - tan beta/1+tan alpha (tan beta)

EXAMPLES:

1)Find the exact value of tan15 degrees+tan30 degrees/1-tan15 degrees(tan30 degrees)
= tan(15 degrees + 30 degrees)
= tan(45 degrees)
= 1

2)Find tan(alpha+beta)
tan alpha=2 tan beta=1
tan(alpha+beta) = tan alpha+tan beta/1-tan alpha(tan beta)
= 2+1/1-(2)(1)
= 3/-1
= -3

Reflection 23

This chapter is full of formulas and you must know the trig chart, if not you can not work just about any problem. Most of the formulas are almost the opposite of each other.



sum and difference formulas for sine and cosine

cos(a±B)=cos(a)cos(B) ± sin(a)sin(B)
sin(a±B)=sin(a)cos(B) ± cos(a)sin(b)




sum and difference formulas for tangent

tan(a+B)=(tana+tanB)/(1-tanatanB)
tan(a-B)=(tana-tanB)/(1+tanatanB)



half angle and double angle formulas

sin2a=2sinacosa
cos2a=cos^2a-sin^2a=1-2sin^2a=2cos^2a-1
tan2a=2tan∂/(1-tan^2a)
sina/2=±√((1-cosa)/2)
cosa/2=±√((1+cosa)/2)
tana/2=±√(1-cosa)/(1+cosa)=sin∂/(1+cosa)=(1-cosa)/sina

Ex problem: Find the exact value of cos25 cos5-sin 25 sin5.

1. You use the sum and difference formulas for sine and cosine.

2.Then you add 25 + 5 when you look at the formula and that gives you sin 30.

3. When you look at the trig chart sin 30 gives you 3/2 as your answer.


One thing I dont not get at all is the half-angle formula.

Reflection 22 (Late, i forgot again)

okay so i'ma explain factoring with trig functions....its really easy once you break it down, here we go:

So you jus started breaking a problem down and you end up with 2cos^2x - cosx - 3 and your stuck and don't know what to do......well, factor!

Simplest way is to put the trig function away for a lil bit and replace it with say...x.

So you have: 2x^2 - x - 3 now jus factor like normal:
(2x^2 -3x) + (2x - 3)
x (2x - 3) + (2x - 3)
x = -1 x = 3/2

Now bring back your trig fuction...
cosx = -1 cosx = 3/2

Now use your unit circle
x = Pi and your other x is no solution because cosine cannot have a value of more than 1.

So when you get to the point where you need to factor trig functions just remember to break it down and replace the trig function with a variable, but after you factor don't forget to finish, like when you get cos = 1 don't leave it as that solve it all the way --- pi.

_____________________________________________________
Still havin trouble wit the half angle formula.

reflection

Hey guys how is everyone day going? My day is going quit swell. There nothing more i would like to do then study math with my closest friends on my MLK holiday. GO MATH! Today we are reviewing everything in chapter ten cause we need a very good grade for our math test. The sum and difference formula for cosine and sine are:cos(alpha+-beta)=cosalphacosbeta-+sinalphasinbeta sin(alpha+-beta)=sinalphacosbeta+-cosalphasinbeta

half angle and double angle formulas:sin2(alpha) = 2sin(alpha) cos(alpha)
cos2(alpha) = cos^2(alpha) - sin^2(alpha) = 1 - 2sin^2(alpha) = 2cos^2(alpha) - 1
tan2(alpha) = 2tan(alpha)/1 - tan^2(alpha)
sin(alpha)/2= + or - sq. root of (1-cos(alpha)/2)
cos(alpha)/2=+or- sq. root of (1 + cos(alpha)/2)

Rewriting a Sum or Difference as a Product:sin(x) + sin(y) = 2sin(x+y/2)cos(x-y/2)
sin(x) - sin(y) = 2cos(x+y/2)sin(x-y/2)cos(x) + cos(y) = 2cos(x+y/2)cos(x-y/2)
cos(x) - cos(y) = -2sin(x+y/2)sin(x-y/2)

sum and difference formulas for tangent:tan(∂+ß)=(tan∂+tanß)/(1-tan∂tanß)
tan(∂-ß)=(tan∂-tanß)/(1+tan∂tanß)


We will be studying and doing many multiple problems with these formulas for the next few hours. We all are hoping that we can get a decent grade on this test.And reminder and basic common sence to all, study your TRIG CHART!!!!!!!!!!!!!!!!!

reflection 22

Okay, so this week was pretty easy. All we did eas review for this giant chapter 10 test tomorrow:/ There are so many formulas for every little thing, its so aggravating. So heres the Double-Angle and Half-Angle Formulas.
*sin2a-2sinacosa
*cos2a=cos^2a-sin^2a=1-2sin^2a=2cos^2a-1
*tan2a=2tana/1-tan^2a
*sin a/2=+or- squareroot of 1-cosa/2 cos a/2=+or- squareroot of 1+cosa/2
*tan a/2=+or- squareroot of 1-cosa/1+cosa=sina/1+cosa=1-cosa/sina


1) If you are given an angle with a decimal you use the half-angle formula. To find a you multiply by 2. Find the exact value of sin 22.5.
a=2(22.5)=45degrees
sin a/2= +or- squareroot of 1-cosa/2
=+or-squareroot of 1-cos45/2
=squareroot of (2/2) 1-squareroot of 2/2/2
=squareroot of 2-squareroot of 2/2 over 2 all over 2/1
then you would sandwich all of that mess....
and get squareroot of 2-squareroot of 2/4
then your final answer would be....

squareroot of 2-squareroot of 2/2


2)Find the exact value of 2sin15cos15=sin2a
=sin2(15)
=sin30
=1/2

Reflection 22

Okay, so I kinda forgot to do a blog last night because of the three-day weekend thing, but here it is. This week was very good, because we only had 3 days of school, but we still managed to get a lot done in math class. We basically reviewed for our chapter 10 test, which i am hoping to do very well on tomorrow. So I'm going to review a few things in Chapter 10.

Sum and Difference Formula for Cosine

cos(alpha +- beta) = cos(alpha) cos(beta) -+ sin(alpha) sin(beta)

Find the exact value of cos 75
alpha = 45 beta = 30
cos(a + b) = cos(a)cos(b)-sin(a)sin(b)
cos 75 = (sqrt of 2/2)(sqrt of 3/2) - (sqrt of 2/2)(1/2)
cos 75 = (sqrt of 6 - sqrt of 2)/4


The only thing I'm gonna have trouble with is learning all of the formulas, and then maybe those problems where you have to edit the formula for example sin 4a = blank, or something like that...if there could be any example problems for this, that would be very much appreciated. Thanks.

Reflection 22

reflection

this week went by like a breeze, if only every week went like that :/
anyways.....since i cant ramble on and stuff anymore to hit the 250 mark........i guess i should get to the math part ............ya......................that thing....with numbers....
anyways, this week, we mainly did formulas and stuff, it was a little confusing at first, but it got rly easy at the end

some of the formulas were

sum and difference formulas for tangent

tan(∂+ß)=(tan∂+tanß)/(1-tan∂tanß)
tan(∂-ß)=(tan∂-tanß)/(1+tan∂tanß)

sum and difference formulas for sine and cosine

cos(∂±ß)=cos(∂)cos(ß) ±* sin(∂)sin(ß)
*opposite of the ± on the left side of the formula

sin(∂±ß)=sin(∂)cos(ß) ±* cos(∂)sin(ß)
* same as the ± on the left side of the formula

half angle and double angle formulas

sin2∂=2sin∂cos∂
cos2∂=cos^2∂-sin^2∂=1-2sin^2∂=2cos^2∂-1
tan2∂=2tan∂/(1-tan^2∂)
sin∂/2=±√((1-cos∂)/2)
cos∂/2=±√((1+cos∂)/2)
tan∂/2=±√(1-cos∂)/(1+cos∂)=sin∂/(1+cos∂)=(1-cos∂)/sin∂


blah, alot of formulas and the trig chart for this chapter.....*sarcasticly* yay....-.-

Reflection #22

Alrightyyy, this week was pretty easy, because all we did was review all of the formulas and stuff. We were off most of the week, so maybe that is the reason why it feels like i didn't learn anything.
_________________________________________________________________________

DOUBLE AND HALF-ANGLE FORMULAS

sin2(alpha)=2sin(alpha) cos(alpha)
cos2(alpha)=cos^2(alpha)-sin^2(alpha)=1-2sin^2(alpha)=2cos^2(alpha)-1
tan2(alpha)=2tan(alpha)/1-tan^2(alpha)
sin(alpha)/2= +or- sqrt of (1-cos(alpha)/2)
cos(alpha)/2=+or- sqrt of (1+cos(alpha)/2)
tan(alpha)/2=+or- sqrt of (1-cos(alpha)/1+cos(alpha)=sin(alpha)/1+cos(alpha)=1-cos(alpha)/sin(alpha)

EXAMPLE:

IF you are given an angle with a decimal you use the half-angle formula. To find alpha, you multiply by two.

Find the exact value of sin22.5

alpha=2(22.5)
alpha=45
______________________________________________________________________

Rewriting a Sum or Difference as a Product

sin(x) + sin(y) = 2sin(x+y/2)cos(x-y/2)
sin(x) - sin(y) = 2cos(x+y/2)sin(x-y/2)
cos(x) + cos(y) = 2cos(x+y/2)cos(x-y/2)
cos(x) - cos(y) = -2sin(x+y/2)sin(x-y/2)

^^here is some more formulas that we need to memorize for the test on tuesdayyy.
______________________________________________________________________

Now, for the stuff that i didn't get, was plugging in some of the formulas. IF anyone wants to show me some more problems, then go right ahead, i need as much help as i can get before the test. Please and THank YOu!

Reflection #22

First, to review, the trig chart:

0 = 0 degrees
pi/6 = 30 degrees
pi/4 = 45 degrees
pi/3 = 60 degrees
pi/2 = 90 degrees

sin 0 = 0
sin 30 = 1/2
sin 45 = square root of 2 over 2
sin 60 = square root of 3 over 2
sin 90 = 1
cos 0 = 1
cos 30 = square root of 3 over 2
cos 45 = square root of 2 over 2
cos 60 = 1/2
cos 90 = 0
tan 0 = 0
tan 30 = square root of 3 over 3
tan 45 = 1
tan 60 = square root of 3
tan 90 = undefined
cot 0 = undefined
cot 30 = square root of 3
cot 45 = 1
cot 60 = square root of 3 over 3
cot 90 = 0
sec 0 = 1
sec 30 = 2 square root of 3 over 3
sec 45 = square root of 2
sec 60 = 2
sec 90 = undefined
csc 0 = undefined
csc 30 = 2
csc 45 = square root of 2
csc 60 = 2 square root of 3 over 3
csc 90 = 1

Now, examples:
**a=alpha

4 sin pi/6 cos pi/6
=2 sin 2a
=2 sin 2(pi/6)
=2 sin(pi/3)
=2(square root of 3 over 3)
=square root of 3

cos^2 x/2 - sin^2 x/2
=cos 2a
=cos 2(x/2)
=cos x

For what I don't understand this week, I'm not sure how to do problems like #s 7b, 7c, and 9a on the chapter 10 review. If you'd work one of these problems out for me, that'd be great. ^^

Reflection

Here is a quick review of our half angle formula and sum and difference formulas

half angle and double angle formulas:sin2(alpha) = 2sin(alpha) cos(alpha)
cos2(alpha) = cos^2(alpha) - sin^2(alpha) = 1 - 2sin^2(alpha) = 2cos^2(alpha) - 1
tan2(alpha) = 2tan(alpha)/1 - tan^2(alpha)
sin(alpha)/2= + or - sq. root of (1-cos(alpha)/2)
cos(alpha)/2=+or- sq. root of (1 + cos(alpha)/2)

Rewriting a Sum or Difference as a Product:sin(x) + sin(y) = 2sin(x+y/2)cos(x-y/2)
sin(x) - sin(y) = 2cos(x+y/2)sin(x-y/2)cos(x) + cos(y) = 2cos(x+y/2)cos(x-y/2)
cos(x) - cos(y) = -2sin(x+y/2)sin(x-y/2)

sum and difference formulas for tangent:tan(∂+ß)=(tan∂+tanß)/(1-tan∂tanß)
tan(∂-ß)=(tan∂-tanß)/(1+tan∂tanß)

reflection

this week went by pretty fast... being that it was only 3 days... but we worked on chapter 10, which was mostly identities and formulas

sum and difference formulas for tangent

tan(alpha + beta) = tan(alpha) + tan(beta)/1 - tan(alpha) tan(beta)
tan(alpha - beta) = tan(alpha) - tan(beta)/1 + tan(alpha) tan(beta)

sum and difference formulas for sine and cosine

cos(alpha + or - beta)=cos(alpha) cos(beta) - or + sin(alpha) sin(beta)
sin(alpha + or - beta)=sin(alpha) cos(beta) + or - cos(alpha) sin(beta)

half angle and double angle formulas

sin2(alpha) = 2sin(alpha) cos(alpha)
cos2(alpha) = cos^2(alpha) - sin^2(alpha) = 1 - 2sin^2(alpha) = 2cos^2(alpha) - 1
tan2(alpha) = 2tan(alpha)/1 - tan^2(alpha)
sin(alpha)/2= + or - sq. root of (1-cos(alpha)/2)
cos(alpha)/2=+or- sq. root of (1 + cos(alpha)/2)

tan(alpha)/2=+or- sq. root of (1 - cos(alpha)/1 + cos(alpha) = sin(alpha)/1 + cos(alpha) = 1 - cos(alpha)/sin(alpha)

im a little shaky on remembering all of this stuff, and i suck at remembering the trig chart

reflection

DOUBLE AND HALF-ANGLE FORMULAS:
sin2(alpha)=2sin(alpha) cos(alpha)
cos2(alpha)=cos^2(alpha)-sin^2(alpha)=1-2sin^2(alpha)=2cos^2(alpha)-1
tan2(alpha)=2tan(alpha)/1-tan^2(alpha)
sin(alpha)/2= +or- sqrt of (1-cos(alpha)/2)
cos(alpha)/2=+or- sqrt of (1+cos(alpha)/2)
tan(alpha)/2=+or- sqrt of (1-cos(alpha)/1+cos(alpha)=sin(alpha)/1+cos(alpha)=1-cos(alpha)/sin(alpha)

Difference Formula for Tangent:
tan(alpha-beta)=tan(alpha)-tan(beta)/1+tan(alpha) tan(beta)

Sum Formula for Tangent:
tan(alpha+beta)=tan(alpha)+tan(beta)/1-tan(alpha) tan(beta)

Sum and Difference Formulas for Cosine and Sine:
cos(alpha+or-beta)=cos(alpha) cos(beta)-or+sin(alpha) sin(beta)
sin(alpha+or-beta)=sin(alpha) cos(beta)+or-cos(alpha) sin(beta)



Example of Sum Formula for Cosine:

cos 75 cos 15 + sin 75 sin 15=
cos (75-15) = cos 60 = 1/2

_____________________________________________

Questions:

#'s 3 and 4 on homework, i know b-rob explained them, but i still don't get them!!!

help???

Reflection

This week we learned more about chapter 10. We learned some new formulas and took quizzes on those formulas. I find the tangent formulas are very easy so i'll give some examples of those. But for chapter 10 it is very important to know your trig chart and your chapter 8 identities.

+Sum Formula for Tangent
tan(alpha + beta) = tan alpha + tan beta/1-tan alpha (tan beta)

+Difference Formula for Tangent:
tan(alpha - beta) = tan alpha - tan beta/1+tan alpha (tan beta)

EXAMPLES:

1)Find the exact value of tan15 degrees+tan30 degrees/1-tan15 degrees(tan30 degrees)
= tan(15 degrees + 30 degrees)
= tan(45 degrees)
= 1

2)Find tan(alpha+beta)
tan alpha=2 tan beta=1
tan(alpha+beta) = tan alpha+tan beta/1-tan alpha(tan beta)
= 2+1/1-(2)(1)
= 3/-1
= -3

I figured that was one of the easiest thing we learned. But if anyone wants to help me out with example like #9 from the chapter 10 test in the book, that would be great. :)

REFLECTION #22

Well this week we barely had school so we didn't really learn anything new. We just sorta reviewed the things from Chapter 10. And we worked on the Chaper 10 test in the book too. Sooo that was fun I suppose. Anyway, I'll just review a few things that I think are super easy. And it'll help me kinda study for the test on Tuesday. Okay so here's a few examples of things that will probably show up on the test.

Ex. 1.) Find sin (45 - x) - sin (45 + x)
*First looking at this problem you know that it is condensed. You're going to have to expand the left side out using the sine difference formula. (a = alpha; b = beta) >> sin (a - b) = sinacosb - cosasinb (*and then after, you'll use the sine sum formula to expand the right side of the equation)
*So for the left side: a is 45 and b is x
*All you do is plug in 45 and x into the formula like this:
* = sin45cosx - cos45sinx
*Then you simplify the things you can by using the trig chart.
(sine and cosine of 45 are both sqrt of 2 over 2)
*So you get > (sqrt of 2/2 cos x - sqrt of 2/2 sin x)
*Now you can expand the right side of the problem by using the sum formula for sine.
*Then you get > (sin45cosx + cos45sinx)
*Then you put both sides of the equation together and solve:
(sin45cosx - cos45sinx) - (sin45cosx + cos45sinx)
*remember to distribute the negative to the right side
*sqrt of 2/2 cosx - sqrt of 2/2 sinx - sqrt of 2/2 cosx - sqrt of 2/2 sinx
*the sqrt of 2/2 cos x's cancel out
*then you add the two sqrt of 2/2 sin x's and get -2sqrt of 2/2sinx
*and that simplifies to -sqrt of 2 sinx (*and those aren't dashes (-) its negative)

Ex. 2.) 2cos^2 pi/12 - 1 Simplify the expression.
*The first thing you want to do is ask yourself what formula this problem looks the most like
*And that would be the cos2alpha formula.
*First you have to change pi/12 to degrees by multiplying it by 180/pi and you get 15 degrees
*15 degrees is "alpha" in the formula, so you just plug it in cos 2alpha
*So you get cos 2(15)
*which equals cos 30
*and by using the trig chart, cos 30 is square root of 3/2

Ex. 3.) (1 + tan^2 y)(cos 2y - 1) Simplify the expression.
*Okay the first thing you should notice with this problem is that 1 + tan^2 y is an identity we learned in Chapter 8.
*So the first parenthesis changes to (sec^2 y)
*In the second parenthesis you can change cos 2y to one of the three formulas in the book.
*The easiest formula to use is the 1 - 2sin^2 y formula so it can cancel out the 1's
*So for the second parenthesis you get (1 - 2sin^2 y - 1)
*The 1's cancel out and you're left with (-2sin^2 y)
*So now your problem looks like this: (sec^2 y)(-2sin^2 y)
*Now you have to multiply these two things together, but to make it simpler you can put secent in terms of cosine.
*sec^2 y now becomes 1/cos^2 y
*So to multiply it you get: 1/cos^2 y x -2sin^2 y/1 ("x" is multiplication here)
*And that gives you -2sin^2 y/cos^2 y
*Then you use identities again. Sin^2 y over cos^2 y equals tan^2 y
*And you bring down the -2. Your final answer is -2 tan^2 y

Alright well I'm done with examples for this week. And surprisingly I'm not really confused about anything in Chapter 10. I'm pretty sure I understand everything. Yay (:

reflection 23

This week was pretty fast, and we didnt learn anything new.

Formulas:
sin(a+b)=sinAcosB + cosAsinB
cos(a+b)=cosAcosB - sinAsinB
tan(a+b)= tanA+tanB
---------
1-tanAtanB





find the exact value of sin 15* *=degrees
{=square root

sin(45*-30*)=sin45*cos30*-cos45*sin30*
=({2/2)({3/2)-({2/2)(1/2)
= {6 - {2
-------
4