My best learning moment this week was when I learned that the sine law can be re-arranged for solving a side vs solving for an angle. This is cool because it is a faster way to solve a triangle than to split it in half and solve for the sides and angles one at a time. Knowing this is helpful because it is a more efficient way of solving triangles and is also simple, as long as you type everything into your calculator correctly.

This week my best learning moment was when I learned the relationship between the sine, cosine, and tangent ratios regarding the unit circle. I find it interesting how, because the radius is always one in a unit circle, the x value represents the cosine ratio and the y value represents the sine ratio. The tangent ratio is the sine ratio divided by the cosine ratio. this is cool because it is a faster way to notice what each ratio is equal to.

My best mistake this week was when I was trying to calculate the rotation angle from the reference angle and I forgot that it is only calculated from a horizontal line and not a vertical line. Now I know that you are only able to caculte the rotation angle off of a horizontal line. for example lets say the reference angle is x degrees, in quadrant I the angle would be x degrees, in quadrant II the angle would rotate to (180 – x) degrees, in quadrant III the angle would become (180 + x) degrees, and in quadrant IV the angle would be (360 – x) degrees.

This week when we were working on word problems, specifically the ones involving distance speed and time, I was having trouble finding out what x would be. this was because there were multiple spots in the table I drew that were not filled out based on the information given. I now know that I am supposed to fill out the table and as long as I have two of the three things I can figure out what is missing based on the relationship between distance speed and time.

This week my best mistake that led to a learning moment was when we were simplifying expressions with adding and subtracting. I thought when you found the common denominator you take all the factored terms from both denominators. this is technically not wrong as long as you multiply the top of each fraction by the same thing, but I was doing more work than I had to. I now know that when there is a common term on the bottom of both fractions, you only put it once in the denominator and any other terms or numbers the two fractions do not have in common. after this you can continue with simplifying the expression.

This week my best mistake that led to a learning moment was when we were in groups at the whiteboards and we were supposed to find out what x is not allowed to equal based on what the denominator is. I only put what zero could not equal based on the final answer, but I then found out I should be using the factored form of the denominator before it is simplified, to get all of the values x cannot equal.

My biggest lightbulb moment this week was when we went to the boards to work on evaluating inequalities. I didn’t remember how to do it because I thought you first had to isolate x. I was able to figure out you are meant to put the constants on one side and anything with an x on the other side and evaluate the expression from there by using algebra once the terms are combined.

This week my biggest lightbulb moment is when it was pointed out to me that you are able to get the vertex form/standard form from factoring an equation by completing the square. This was really cool to me because it means that I am able to save time when factoring, and I will be able to find the vertex much faster since it shows the vertical and horizontal translations.