Parametric Equations Using Trig Functions (2/18)

In class, we discussed conics and their equations in three dimensions. We began using trigonometry to find both the three dimensional and rectangular equations for the conics. We also discussed the relationship between the graphs of the trigometric functions and the resulting graph of the conic when they are used in the equations.

Parametric Equations

In class today we learned about parametric equations. Right now, when given 2 equations we are supposed to graph them on our calculator to figure out the general shape of the graph. Then by using the Brute Force Method, we can find out the rectangular equation for the graph.

Notes for Feb 8

In class we learned about graphing with three variables, involving multiple dimensions.

We learned some of the common graphs you can make with three variables, as well as how to make them. We learned the standard form of these equations as well as how to use these equations to find the velocity of the line, the speed, and the slope.

Parabolas

Today in class we talked about parabolas. Mr. Vischak showed us a picture of a parabola, a hyperbola, and an elipse on his computer. There were two lines on each of these graphs. One connecting from the vertex and one from the focus. We learned another way to write eccentricity. mAB/mAC, with A B and C being the vertex focus and directrix respectively. We also learned how to write parabolic equations. y=a(x-h)^2+k is the standard form.

Hyperbolas- 2/10

Today we discussed hyperbolas, which can be confusing (especially the slope of their asymptotes), but once you memorize their properties you will dominate them.

Ellipses

Today we checked the worksheet and reviewed ellipses.

Notes for 2/3

Today we talked about the dot product of two vectors. Basically, if you have two vectors and want to find the dot product of them, you have to take the first term of each and multiply them together and add that to the second terms multiplied together (the dot product of vector "a" and vector "b" would be a1*b1 + a2*b2). We also learned the equation to find the angle between two vectors, as shown in the notes. By applying what we learned today about dot products and what we learn previously about vectors' magnitudes, we could figure out the angle. We proceeded to do a practice problem with this concept. Something to note about dot products is that if the dot product of any two vectors =0, the vectors are orthogonal (perpendicular in more than two dimensions). Another important thing is the diagram in the upper right-hand corner of the notes.

Notes for 2-2

Today we talked more about vectors especially how to combine them. We worked through several types of practice problems which all required you to be able to combine vectors. For example, one type of problem gives you 2 vectors and ask for a third which, when combined with the other 2, gives you a vector with 0 magnitude. For those, you add the i and j components of your vectors and the final one will have the same value but with the opposite symbol(+/-). Another type of problem we solved asked for the vector that would result when multiple vectors are combined. For those you just add the i and j components and if you need the angle, it helps to draw it out and think of the i component as the x value and the j component as the y value. One thing to note is that these problems are very similar to physics problems that involve vectors of forces.

Notes on 2/1

In class that day we learned about how to find the magnitude of a vector and how to find different components of vectors with magnitudes larger than one. We did a few example problems and we ended with a physics type problem in which a ball is thrown and we use vectors to find its maximum height. We also learned how to use "i" and "j" instead of the standard component form.