Law of Cosines

Here is a site that explains the law of cosines really clearly

Adan D- More on the Law of Sines and Oblique Triangles

Here is a site that explains the Law of Sines and gives an example.
http://math.info/Trigonometry/Law_of_Sines/

The Ambiguous Case (SSA)

This case is for two sides and a nonincluded angle (SSA). Since there are several possibilities this case is called the Ambiguous case. I found a website that makes it a bit clearer than the book does, at least for me!

http://www.regentsprep.org/Regents/math/algtrig/ATT12/lawofsinesAmbiguous.htm

Another way to look at laws of sines and cosines

I saw this site and it was helpful to see another way that laws of sines and cosines were explained. Take a look at this!

http://www.clarku.edu/~djoyce/trig/laws.html

Need Extra Help with the Law of Sines???

Khan Academy is a great website because you can watch lectures and you can rewind and replay parts if you don't quite understand them.

Here you can review the law of sines: http://www.khanacademy.org/v/proof--law-of-sines?p=Trigonometry

go to http://www.khanacademy.org/ and scroll down to find more help and more lessons.

If you think Trig is unimportant think again!!!

I came across this website yesterday and thought some of you might like to read it.

http://www.mathworksheetscenter.com/mathtips/trigonometry.html

Good website for learning and honing skills on verifying identities

http://www.karlscalculus.org/trigid_examples.html

This website will help you through the steps to verify identities. It is a good website to review for the test which is coming up on Tuesday.

Great Website

Class, I found a great site to help with learning the trig identities and using the strategies. This is a very clear site and would be helpful for anyone.

http://www.sosmath.com/trig/Trig5/trig5/trig5.html

Scribe Post 4/18/11

Today John Henry showed us some strategies for proving identities. This is also in the book chapter 3.2.

The first strategy we learned was for proving an identity when you have fractions.

Multiply denominator and numerator by the numerator of the opposite side.
Cos^2+sin^2=1 - Pythagorean Identity.
Second strategy - Splitting Fractions with + or - in numerator.

Also below this post Irfan shared a great website on all the strategies for proving identities. Looking at that website was the most helpful for me. I recommend anyone who is having trouble with these to look at this website. It's very simple and well written. A good way to memorize these strategies and identities is flash cards! We have a final coming up soon so I suggest you do that!

Next Scribe: Elijah

Scribe Post 4/18/11

1. Today John Henry showed us some strategies for proving identities. This is also in the book chapter 3.2.

The first strategy we learned was for proving an identity when you have fractions.

Multiply denominator and numerator by the numerator of the opposite side.
Cos^2+sin^2=1 ---> Pythagorean Identity.
Second strategy - Splitting Fractions with + or - in numerator.

Also below this post Irfan shared a great website on all the strategies for proving identities. Looking at that website was the most helpful for me. I recommend anyone who is having trouble with these to look at this website. It's very simple and well written. A good way to memorize these strategies and identities is flash cards! We have a final coming up soon so I suggest you do that!

Next Scribe: Elijah

Irfan Fazal Website Help for verifying trig identities

http://www.karlscalculus.org/trigid_examples.html

This is a website I found which is great to help you on verifying trig functions if you don't feel comfortable with them yet. They will be on the final, so take some time to understand them.

Scribe Post 4/13/11-Adan D.

Today we learned how to prove and not prove identities. We learned the steps and we did examples. Steps(proving not an identity): 1) Plug a value into each side of the equation 2) Simplify both sides 3) check and see if they equal each other. Steps (proving an identity): 1) start with the more complicated side of the equation 2) use cos/sin to simplify 3) other strategies like factoring, and foiling may help. We also learned that you need to know the identities in order to be able to prove identities. Two examples we did are 2sin=sin(2) and 1+secx sinx tanx= sec^2x.

Next Scribe: Alex

John Henry Scribe Post April 12, 2011

Today in class we went over homework involving Identities. Incase you haven't learned them here is a link to Kelsey's Scribe Post about them.

These are Odd/Even Identities:

sin (–x) = –sin x cos (–x) = cos x tan (–x) = –tan x

csc (–x) = –csc x sec (–x) = sec x cot (–x) = –cot x

These are the Basic Identities:

These are the Pythagorean Identities:

sin² θ + cos² θ = 1

tan² θ + 1 = sec² θ

cot² θ + 1 = csc² θ

Next Scribe: Irfan

Kelsey Scribe Post: April 11, 2011

Today in class we learned more about the basic identities, which consist of:

We did some practice problems/ problems from our homework that showed how to write functions in terms of another, how to use these identities to find other function values and how to simplify identities.

We focused on example problem 3 in the book (Pg 168) and went through the steps to solve. (steps are in book, also)

We also briefly learned about odd and even identities (pg 169) and how to classify a function as odd or even.

Next scribe: John henry? not sure.

Elijah Scribe Post - 3/31/11

Today in class, we talked about An identity is an equation that is satisfied by every number for which both sides are defined. Identities can help combine terms when dividing and multiplying. There are infinitely trigonometric identities, but only the most common identities should be memorized.

Reciprocal Identities

sin(x)=1csc(x) cos(x)=1sec(x) tan(x)=1cot(x)
csc(x)=1sin(x) sec(x)=1cos(x) cot(x)=1tan(x)

Tangent and Cotangent in Terms of Sin and Cosine

tan(x)=sin(x)cos(x)
cot(x)=cos(x)sin(x)

Pythagorean Identities

sin2(x)+cos2(z)=1
1+cot2(x)=csc2(x)
tan2(x)+1=sec2(x)

Odd/Even Identities

An odd function is one for which f(-x)=-f(x) and an even function is one for which f(-x)=f(x)
Odd Identities:

sin(-x)=-sin(x)
csc(-x)=-csc(x)
tan(-x)=-tan(x)
cot(-x)=-cot(x)

Even Identities:

cos(-x)=cos(x)
sec(-x)=sec(x)

Scribe Post Alex K. 3/30/11

Today we looked at a cool website that shows the graph of transformations of the sine and cosine functions.

Here's the link http://members.shaw.ca/ron.blond/sc.APPLET/index.html

This website was pretty neat to see and it was helpful for me, being a visual learner. We also learned that the sine of x is the exact opposite graph as the cosecent, so if the graph starts off above the x axis and drops down below for the sine of x, the cosecent of x it will start off below the x axis and rise up above the x axis. Rise up like the falcons were supposed to do against greenbay.... anyways on a better note, today was a productive day and the website is VERY helpful and helps you understand better what we are learning.

Next Scribe: Elijah

Scribe Post -Adan D: March 29, 2011

Today we learned more about graphing sine, and cosine, functions. On the unit circle:

sin α= y cosα=x tanα=y/x cscα= 1/y secα=1/x cotα=x/y

We also learned how amplitude changes the y values of the graph and how it is always positive. We also learned about the graph's period, which is the interval it takes for a sin or cos function to complete one cycle. Here is an example of a sine function:

Kelsey's Scribe Post March 28

Today we learned about the sine function, the equation y=a sin t, amplitude and the unit circle.

Jojo showed us this cool website that demonstrates the sine function.

http://www.intmath.com/trigonometric-graphs/1-graphs-sine-cosine-amplitude.php

and the cosine function (at the bottom of the above website)

Here is an example of a unit circle:

http://www.regentsprep.org/Regents/math/algtrig/ATT5/unitcircle.htm

SOHCAHTOA

SOHCAHTOA

Sine Opposite Hypotenuse

Cosine Adjacent Hypotenuse

Tangent Opposite Adjacent



sin α=a/c
cos α=b/c
tan α=a/b

csc α= c/a
sec α= c/b
cot α= b/a

Scribe Post March 1st Irfan

Today, we went over problems 1-16 that we had been assigned to finish. Many people in the class were thinking that trig has to do with side lengths, but we learned that it was not side lengths, but ratios. At the end of this post will be a website that you can go on to learn more about trigonometric functions. We also had time to catch up with other work in class.

Can you do Division? Divide a loaf by a knife - what's the answer to that? ~Lewis Carroll, Through the Looking Glass

Here is the link to the website that you can go to for extra help.. You can also google trigonometric functions

http://www.math-mate.com/chapter26_2.shtml

Elijah's Scribe Post - 2/28/11

Today in class we learned about trigonometric functions. Jojo drew a picture of a right triangle on the board and labeled an angle adjacent to the hypotenuse theta. In this triangle, the hypotenuse is labeled r, the vertical leg is y and the horizontal leg is x. Sine, cosine, and tangent are side ratios that you can use to determine unknown angles and sides of triangles. Sine (sin) is the ratio of opposite side over the hypotenuse, or y over r. Cosine (cos) is the ratio of the adjacent side over the hypotenuse, or x over r. And Tangent (tan) is the ratio of the opposite side over the adjacent side, or y over x. This can be remembered by the word SOHCAHTOA which stands for:

Sine
Opposite
Hypotenuse
Cosine
Adjacent
Hypotenuse
Tangent
Opposite
Adjacent


Or as it relates to our math class:

Signs
Of
Hovercrafts
Can
Actually
Harm
Teachers
Of
Arithmetic


Trigonometry is a sine of the times. ~Author Unknown

Alex K. Scribe Post 2/23/11

Today we learned about common angles names. We learned about Θ"Theta", α"Alpha" and β "Beta".

R---> Radius = 1 unit

S----> Arc length

Θ=s/r

Θ can only be in radians using this formula.

Circle=360° or 2πr

Since the central angle and the arc length are the SAME, put the central angle in radians because radians are the same unit as length and the arc length cannot be in degrees.

Learning that the central angle and the arc length are the same is very interesting to me. It seems like it's just a coincidence but it can't be and that's what's so cool about it, that someone took the time and really worked at this and figured it out. It's crazy.

Adan Scribe Post: Day 13- Feb. 22 2011

Today Jojo sarted teaching section 1.2 which is about radian measure. A radian is the measure of and arc's length. He talked about how in the radian system of angular measurement, the measure of one revolution is 2pi, half a circle is pi, each right angle is pi/2 and so on. He also talked about the most common measurements and their degree. Here are some of those:

pi/4 = 45 degrees

pi/3 = 60 degrees

pi/6 = 30 degrees

2pi/3 = 120 degrees

and so on.

Degrees to Radiants

Kelsey Scribe post 2/16

Today we learned about coterminal angles, quadrants and degree measures of angles.

We were taught that there are four quadrants (I, II, III, IV) and how to determine which quadrant an angle lies in.

How to find coterminal angles m(beta) = m(alpha) + k360

Here is a good website that explains everything in depth and clears up alot of confusion

http://www.themathpage.com/atrig/measure-angles.htm

example of coterminal angles

John Henry Scribe Post 2/9/2011

Today Jojo explained the quadratic formula F(x)= ±a(x±h)±k

F(x)= ±a(x±h)±k

determines where on the x axis the shape is

determines where on the y axis the shape is

Whether or not on x axis

a >1 stretch

01

here is a website with some great examples:

http://uncw.edu/courses/mat111hb/functions/inverse/inverse.html

you can also use page 33 in your book

next scribe: Kelsey

How to determine if two functions are inverses of each other....

Elijah Scribe Post - 2/8/11

Today we discussed functions. We had a long debate about whether the area of a circle is a function. We came to the conclusion that a circle is not a function because it has more than one value for x for each value of y. Since it is the day after the Super Bowl, I decided to find out if the area of the outline of a football is a function. It also is not a function because of the same reason as a circle.

Scribe Post Feb. 8th Irfan

Today we talked about Parent Functions, which we have all covered in other classes. The parent functions are x squared, square root of x, x cubed, absolute value of x, and x. We also spent some times going over an example in the book that relates to the diagonal compared to the are of a square. We had about 25 minutes to do our homework so I hope we were all productive.

Types of functions
x-squared function f(x)=x2
Square-root of x f(x)=x
Cubed function f(x)=x3
Absolute value function f(x)=x

X function (bottom line) f(x)=x

We discussed making a function from a diagonal of a square. We decided that the best way would be to use the pythagorean theorem with the sides as the legs and the hypotenuse as the diagonal. Here are the steps:

s2=A
s2+s2=d2
2s2=d2
s2=d22
A=s2=d22
A=d22

SOURCE: ELIJAH KIRKLAND ANDREWS

Trigonometry is a sine of the times. ~Author Unknown

Next scribe: John Henry Ward