1. The first thing you do is draw and label the triangle. After that you find the correct formula which is tan. Next you plug in the numbers tan(44)=x/23. Then you multiply which will be x=22.218.

2. The first thing you do is draw and label the triangle. Next you find the correct formula which is tan. After that you plug in the numbers tan theta = 16/36. That equals 0.444. Next you do the inverse which will be theta=tan-1(0.444). The answer is theta=23.941.

I will be working problem 3 on the pythagorean theorm side. In order to solve this problem you must use the a^2+b^2=c^2. They gave me the a and c side so i must find the b side. The first thing i do is plug in the numbers which will be 49+b^2=81. Next i subtract 49 from each side and i will be left with b^2 =32. After that you have to do square root and the answer will be 5.657.

The next problem I will be working is number 7 on the trig ratio side. The first thing I do is label the triangle. After that I will find the correct formula which is tan=opp/adj. Then I will fill in my numbers in the equation which is 19/23 and divide it. The next thing you do is the inverse which is tan -1 (0.826). When you put it in the calculator the answer will be 39.559.

This week we learned how to do inverse trig ratios. You do it by solving for theta. For example your solving for cos and you have theta = adj/hyp. The first thing you do is put in the numbers and its going to be theta=20/31. Then you have theta=0.645. After that you put cos-1(0.645) in the calculator. Then your answer is theta=49.834.

Today we learned how to do trig ratios. I understood it pretty well. You solve the problems by first labeling your triangle. There’s a adjacent, opposite, and hypotnuse side. After you label you find which formula to use. You can use sine, cosine, or tangent. After that you solve the equation.

This week we learned about the pythagorean theorm. The formula is A^2+B^2=C^2. You use the formula to solve for the unknown variable. You plug in the know variable into the equation. After you solve the equation you do the square root.

Linear Measure example 2:

find LM . LN = 4 MN = 2.6

1st step: draw the line with the points and numbers in the correct spot

2nd step: put the points in equation form

LM+MN=LN

3rd step: put in numbers for the correct letter

LM+2.6=4

4th step: solve

LM+2.6=4

-2.6 -2.6

LM = 1.4cm

Rotation example 3:

180degrees ccw/cw (-7,3)

1st step: find the formula

(x,y) -> (-x,-y)

2nd step: put in the formula and multiply by -1

(-7,3) -> (-x,-y) -7•-1 3•-1

3rd step: solve

(-7,3)-> (7,-3)

Distance problem 8:

U(1,3) B (4,6)

1 step: put numbers in the formula

d= square root (x2-x1)^2 + (y2-y1)^2

(4-1)^2 + ( 6-3) ^2

step 2: solve

5^2 + 3^2|25+ 9 = 34

Reflection problem 1:

step 1: write the rule

(x,y)-> (x, y•-1)

step 2: make a chart with the points

pre image x y (x,y)

(-3,0) -3 0 (-3,0)

(-4,5) -4 -5 (-4,-5)

(-7,5) -7 -5 (-7,-5)

(-6,6) -6 -6 (-6,-6)

step 3: graph the points

summary:

I learned many new topics this nine weeks. My favorite one was rotations about the orgin because I enjoy graphing. I struggled the most with learning about points, lines, and planes. It was difficult for me because there were alot of definitions that we had to learn and I’m not good with learning them. In conclusion, I learned alot this nine weeks.

This week we learned about rotations. A rotation can go clockwise or counterclockwise. The shape rotations around the orgin. You can turn 90,180, or 270 degrees clockwise or counterclockwise. Each direction has different rules. This shape rotated 90 degrees clockwise.

Im doing problem 2. The first step is to write the rule which is multiply x coordinate by -1. With the rule you multiply all the x’s by -1. The x’s are on the left side and y’s are on the right. The y coordinates stay the same. The second step is to put it in a chart which will look like :

(x,y) | x | y | (x,-y)

A (3,-4) |3•-1= -3| -4 | (-3,-4)

B (1,-6) |-2•-1= 2| -6 | (2,-6)

C (-2,-3) |-2•- 1=2| -3 | (2,-3)

D (3,1) |3•-1 =-3| 1 | (-3,1)

After you make your chart you will plot your preimage points and your image points.

A reflection is the same shape ,but in a different location on a coordinate plane. A reflection includes a preimage and a image. A reflection can go over the x and y axis. In a translation, every point of the shape must be moved in the same direction with the same distance. The shape doesn’t change form in any way.

24. k(2,3) p(4,4)  the first step is to put it in the formula.. square root (4-2)^2 + (4-3)^2 . next you solve it .. 4+1 = square root 5

34. t(3+5/2 , u (1+3/2) the first step is to add both numerator.. (8/2,4/2) next you divide. = (4,2)