This week, in the continuation of the topic of trigonometry, we learned new formulas and things about them. In this section, we learned how to use a calculator to calculate and find the sine, cosine, and tangent of numbers, and what are its different modes.

First, to use the calculator, we must make sure of the mode on it. Make sure the calculator is in Degree or Radian mode, depending on which unit your angle is in.

Sine calculation:
* Enter the angle number.
* Press the “sin” key.
* The result of the sine of the angle is displayed.
(This is the way for all of them sin,cos,tan)

This mode is used to find the external dimensions of the triangle and its sides.

In order to find the problems that ask us the angle and size inside the triangle, we have to use another solution that we use by writing the sine to the negative power of a product of the external numbers outside the triangle.

Example:

Consider a right triangle where one angle measures 30∘and the length of the adjacent side is 8 units. We want to find the length of the opposite side.

This week, I learned many topics that I may have heard about before, but I didn’t have much skill or understanding to solve them or anything else related. One of these topics is trigonometry, which relates to triangles and their angles and degrees. One of the key formulas in this subject is the Pythagorean theorem, which states that a squared plus b squared equals c squared. This is one of the most important formulas used to find the lengths of the sides of right triangles and to determine relationships between them.

Suppose we have a right triangle with one side measuring 3 units and the other side measuring 4 units. To find the length of the hypotenuse (the side opposite the right angle), we use the Pythagorean theorem:

c2=a2+b2

c2=32+42

c2=9+16

c2=25

c=252=5

This was one example of using the Pythagoras formula.

Another topic that is related to this lesson and I got to know it for the first time this year is the topics called (sin) Sine, (cos) Cosine, and (tan) Tangent, which is one of the main foundations of this formula that is used more often. It is a right triangle.

Right Triangle

• A righ triangle is a triangle that has one angle equal to 90 degrees. Typically, this angle is denoted as angle $C$. The other two angles (A and B) can vary, and their sum will be equal to 90 degrees.
• Sine (sin): The ratio of the length of the side opposite to angle $\theta$ to the length of the hypotenuse:

  sin(θ)= The ratio of the length of the side opposite to angle θ\thetaθ to the length of the hypotenuse:
        sin (θ)= length of the opposite side

•                      length of the hypotenuses

•  Cosine (cos): The ratio of the length of the adjacent side to the length of the hypotenuse:
• cos(θ)=length of the adjacent side
•               length of the hypotenuse​

Tangent (tan): The ratio of the length of the opposite side to the length of the adjacent side:

tan(θ)=length of the opposite side= sin(θ)

              length of the adjacent side ​= cos(θ)

• The Pythagorean theorem states that in a right triangle, the following relationship holds:

  a2+b2=c2
  where $c$ is the length of the hypotenuse and a¸ a and b are the lengths of the adjacent and opposite sides, respectively.

• This theorem helps us understand how sine and cosine ratios relate to measuring the lengths of the sides. For example, if we know one side and an angle, we can use these ratios to find the lengths of the other sides.
• One of the ways to make it easier and the most practical things that I learned this week is the word SOHCAHTOA which means mnemonic device used to remember the definitions of the sine, cosine, and tangent functions in a right triangle. Each part of the acronym corresponds to a different trigonometric ratio:
• SOH:
  • Sine = Opposite / Hypotenuse
• CAH:
  • Cosine = Adjacent / Hypotenuse
• TOA:
  • Tangent = Opposite / Adjacent
• these are new thing i learned this week ​

this week math i learned new thing that’s scientific notation-large Numbers

The new lesson I learned this week was about scientific notation, which is used to write numbers that are either very large or very small. I didn’t have any prior knowledge about this topic in previous math classes, so this was the first time I realized that there are ways to represent numbers composed of many zeros more easily and concisely. In this post, I want to explain it to you.

As I mentioned, practical numbers are those where most of the digits are zeros, or the number of digits is so large that it may be difficult for anyone to read them all and assign a unit. For example, the easiest number is 1, which has no tens, no hundreds, and none above that. However, numbers like 1,000,000,000,000 (one trillion) are numbers that are not easy to read, and separating them into groups of three digits may not always be practical. Therefore, to make this number easier and shorter, we can use powers , ten and decimal numbers.

The way to use powers of ten and decimal numbers to represent a large number, especially one where the digit zero is most frequently repeated, in a shorter and more easily readable form is as follows: First, we focus on the given number. For example, the number 34,000,000,000 is not easy to read or count the zeros. Therefore, we need to write this number in a more concise form. In this number, 3 and 4 are the main digits that define the identity of the number. So, to choose the decimal number, we use 3.4.Then, we need to multiply it by 10 and write the number of zeros in the exponent for 10.

By doing this, we can indicate the number of zeros in front of that number based on the exponent we used for 10.

We write 34,000,000,000 in this form:
3.4×1010=34000,000,000

The exponent for 10 represents how many places the decimal point needs to be moved to get back to the original number. For example, in 3.4×10103.4 \times 10.{10}3.4×1010, the decimal point moves 10 places to the right, which effectively adds 9 zeros after the 34 (not 10 zeros).

Some of the applications of these numbers in science and engineering to represent astronomical distances and microscopic sizes.
Statistics for displaying populations and big data.
Numerical calculations to simplify calculations

these are the some of the info from the scientific notation numbers i learend this week

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In the second week of school, in my math class, I learned two new and related topics that I didn’t know much about before, and I want to explain them to you in as much detail as I can in this post.

• One of them is GCF, which means (greatest common factor), which means that it is the largest positive integer that divides two or more integers without a remainder.
• For example, if you want to find the GCF of 24 and 36:
  1. List the factors of each number:
     • Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
     • Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
     • Here we find that the numbers 1, 2, 3, 4, 6, and 12 are found in both of these two numbers factor.
     • To find the gcf of these two numbers, we must find the greatest number in the factors of these two numbers, which is 12, so the gcf of these two
     • numbers is 12.
• The second thing I learned is LCM, LCM is the smallest number that both (or all) of the given numbers can divide into without leaving a remainder.
• List Multiples: Write down a few multiples of each number.
• Find the First Match: The first number that appears in both lists is the LCM.
• Example:

To find the LCM of 4 and 5:

1. Multiples of 4: 4, 8, 12, 16, 20, …
2. Multiples of 5: 5, 10, 15, 20, …

The smallest common multiple is 20.

These are the two thing i did not know about them and i learned them this week

This past summer, the events where I used math were situations such as counting money or increasing or decreasing the amount of taxes and discounts on prices, calculating kilometers, distances, calculating hours for planning, and calculating points. In games like volleyball and other sports, these are the most of my uses of math this summer