Systems of equations

When we have a systems of equation, we can solve it algebraically and also solve with geometry we can graph or use substitution/elimination.  When we have exactly one answer, it means the system is consistent and independent. That means the lines intersect at exactly one point. When we have a infinete number of solutions, it means he lines overlap each other so every point on the lines is a solution. That is called consistent nod dependent.  When we have no solution, which is when lines are parallel toeach other. There is no intersection, so there is no solution.  Then the system is inconsistent.   

My polar equation pic

Polar coordinates.

This week we learned about pole cordintes.  Those are points on a circular graph.  It contains a r and a angle value. When graphing, if the angle is positive, we look counterclockwise, and if the angle is negative, we count clockwise. We could switch polar and rectangular coordinates back and force. From polar to rectangular, we use x=rCosø and y=rsinø to get x and y value 

Parabola

This week we talked about prabola. Prabola is a u shape graph either going up and down or left or right. Parabolas have derixtrice.  It also has a focus.  The directrix for vertical graphs is y=k-c and for horizontal graph is x=h-c.  The prabola is symmetric, and there is a axis of symmetry.  The equation for parabola is (x-h)^2=4c(y-k).  If the graph is side to side, the equation's x and y switches.  The focus is (h, k+c) and vertices is (h,k).   

rotating conic

When we graph a conic graph that is tilted, we could try to rewrite it back into the normal equation.  The equations have angles, to rewrite this equations, we first need to find the angle.  Cot2x=A-C/B.    We get the A,B,C values from the equation given.  Ax^2+Bxy+Cy^2+Dx+ey+F=0. He second step is to replace x and y with x'cosø-y'sinø and x!sinø+y'cosø.  The last step is to plug in the x and y into the equation. After plugging in, we just do algebra and simplify the new equation.   And now we have a new equation for the rotated conic graph.  

2nd semester goals

Last semester, I think I did good on the homework part. I was able to submit my works on time and made sure I try for all the questions.  I also kept my notes well and I think it really helped me when I needed to review for tests.  Things that I didn't do so well was i didn't review well before the tests, especially the earlier tests. The informations were too much for me to remember without looking back at the notes for several times.  But when the semester was near ending, I realized I need to review more, and I felt note confident on the tests than before.  For this new semester, I want myself to be more focused on study and make sure to arrange times for reviewing and finish my works on time.  

During my break, I went to Disneyland on Christmas Day, it was fun. There were a lot of people. 

Law of Sines/Cosines

Mary Christmas :)!!!!!

Law of sine is used when given at least 2 sides and one angle, or given 2 angles and one side. Law of cosine is used when given three sides, or three angles, or one angle and two sides. When we solve a problem, we better just use law of cosine one. And continue the problem using law of sines. Because the law of cosine is more complicated than law of sine, we can avoid unassary calculation errors by choosing a simpler method. Law of sines is that the fraction of one side and it's opposite angle is proportional to the other set of angle and side.  Law of cosine is a^2=b^2+c^2-2bc CosA.  And same for solving other sides.