Factoring is like removing the GCF also known as just Expanding

To “expand” a polynomial question you need to multiply the number outside of the brackets by the numbers inside the brackets.

How to find angles:

sin(θ)=​

Where:

• $\theta$ is the angle.
• “Opposite” is the side opposite to the angle.
• “Hypotenuse” is the longest side of the triangle.

To find the angle:

θ=sin⁡−1

Use the inverse sine (sin⁻¹) to calculate the angle.

Using Cosine (cos):

cos⁡(θ)= ​

Where:

• “Adjacent” is the side next to the angle.
• “Hypotenuse” is the longest side of the triangle.

Use the inverse cosine (cos⁻¹) to find the angle.

θ=cos−1

Using Tangent (tan):

tan⁡(θ)=

• “Opposite” is the side opposite the angle.
• “Adjacent” is the side next to the angle.

To find the angle:

θ=tan⁡−1

 

This week’s class taught us trigonometry and how to use a scientific calculator.

We learned the three main trigonometric ratios: sine (sin), cosine (cos), and tangent (tan).

Also known as SOA CAH TOA

These ratios help relate a triangle’s angles to its sides’ lengths. For example, in a right triangle (a triangle with a 90-degree angle), sin(angle) = opposite/hypotenuse, cos(angle) = adjacent/hypotenuse, and tan(angle) = opposite/adjacent

We learned how to find an opposite angle by the side directly across from the angle you’re focusing on. For example, if you have a right triangle and you’re looking at angle A, then the side opposite angle A is the side directly across from it.

We learned how to find the adjacent side by the side next to the angle you’re considering but not the hypotenuse. In the same right triangle scenario, if you’re looking at angle A, the side adjacent to angle A is the one that is next to angle A but not the hypotenuse.

Scientific notation in math is a way to write very large or very small numbers in a more concise (expressing much in few words) form. It’s often used in science, where numbers can be really big or really small. In scientific notation, a number is written as a coefficient multiplied by 10 raised to a power.

Ex: 3,000,000 can be written in scientific notation as 3 x 10^6.

This form makes it easier to work with such numbers in calculations and comparisons.

0.000000256 m -> spacing inside a computer chip: The very small number can be written in scientific notation to make the number seem smaller.

Ex: 0.000000256 = 2.56 × 10 -7 

• When the number is on the right side of the decimal point, the exponent is written as a negative number. If the number is on the left hand side, the exponent are written as a positive.

Factor trees are a visual way to break down a number into its prime factors. To create a factor tree, you repeatedly divide the number into factors until you reach only prime numbers. Here’s how it works with two examples:

Example 1: Factorizing 60

1. Start with 60:
   • Find two factors of 60, such as 6 and 10.
   • Write 60 at the top and draw branches to 6 and 10.
     
   • Factorize 6:
     • 6 can be broken down into 2 and 3 (both are prime).
     • Draw branches from 6 to 2 and 3.

     Factorize 10:

     • 10 can be broken down into 2 and 5 (both are prime).
     • Draw branches from 10 to 2 and 5.

     Complete Tree:

     • The factor tree for 60 will have the prime factors 2, 2, 3, and 5.

 

 

In the summertime, I went to a Concert at the PNE Forum. I used math when going to the Ken Carson Concert with 2 of my friends and we used math to calculate how much 3 tickets would cost.