Today in class we learned about vectors. We started off class by talking about numbers. We graphed the number 3 on a number line. We found out that you can graph 3 in two ways. The first way is the literal number 3 on a line, so we placed a closed circle on the number 3. The second way we learned was you can use 3 as a value, which is shown on the second number line. We drew closed circles on 2 and 5 and drew a line connecting the two points and drew an arrow showing the direction in which we went. This shows us the difference between a number and a value; one closed circle on the number 3 was the number and 2 closed circles on 2 and 5 was the value 3. We next learned about the Component Form of a vector which goes as follows:

x(with a hat) = (the numbers with the 'a' and 'b' are there for coordinates only)

First off, the "hat" over the x in the picture is there to show that we are dealing with a vector, but on tests vectors will be shown in bold face. Second, we learned that the angled brackets tell us that we are dealing with a vector quantity.

To use the Component Form of a vector, all you have to do is plug in the coordinates for 2 vectors and do the algebra to get your answer.

1/28/09 - Proofs for Law of Sines, Law of Cosines, and more fun stuff...

Today was more of a theoretical class, we worked with 5 problems from the board, 3 proving the Law of Sines, the Law of Cosines, and the Pythargoren thereom, and 2 involving those theorems, some geometry and trig. We started, but didn't finish covering the last two problems, so you can try to figure them out on your own, and wait for the next post to check your work...

one fact we covered in class that was new to me: to inscribe a triangle in a circle, center the circle around the point of intersection of two of the triangle's perpendicular bisectors don't worry about the third, because all three intersect at the same point)

Law of Sines- 1/27/10

In class today, we took notes on the Law of Sines. This formula allows you to solve for the rest of a triangle if you already know an angle, angle, and a side (AAS), or if you know a side, side, and an angle (SSA). This formula allows you to solve for the unknowns of all triangles as long as you have enough given information. When you have an AAS triangle, there is one possible solution, but with SSA triangles, you can have 0, 1, or even 2 possible solutions, so it is important to check if triangle even exists.

The basic formula for the Law of Sines is:

 (a/sinA) = (b/sinB) = (c/sinC) 

Notes 1/26 - Law of cosines

1/26 - And we're back to school. . . Today we took notes on "the law of cosines." This formula allows you to solve for any triangle (find all values for angles and sides) if at least 3 of these values are known. The law of cosines works with any type of triangle - not just right triangles. One thing to remember in notation is that uppercase letters refer to angles and lowercase to sides. In solving for a triangle using the law of cosines it does not matter which value you look for first, as long as you can find the others taking that approach. Also, remember to check if the triangle is even possible in the first place. The following is the formula for law of cosines:

a^2 = b^2 + c^2 - 2bc*cosA