## Week 3 – Math 10

This week we began our unit on trigonometry. One of the things I learned was SOH CAH TOA, abbreviations that help you to memorize how to find side lengths using angles and equations.

Each set of abbreviations begins with a letter that describes the angle equation to use on your calculator (S=sin C=cos T=tan). Depending on the angle of the triangle you are using and what side lengths are given to you, you can choose the correct angle to use.

Each triangle has 3 sides, and when a base angle is given to you, these sides are given names. The longest of them is the hypotenuse, and the side that the base angle sits on is called the adjacent side, the final one, the opposite side, sits on the opposite of the angle.

The other two letters in each abbreviation shows you what sides to use and in what order (OH=opposite/hypotenuse AH=adjacent/hypotenuse OA=opposite/adjacent. \

Even if you only have one side of the triangle and the angles (90 & other), you can find the side length you are looking for.

## Week 2 – Math 10

This week I learned how negative exponents work and how they effect their base’s. Negative exponents unlike positive exponents don’t increase the numbers size. Normal exponents multiply a number over and over (ex. $3^3 = 3\cdot3\cdot3 = 27$) and negative exponents turn the number into a fraction (ex $3$ to the power of $-3 = \frac{1}{27}$).

You can turn it into a normal number by following the next steps. I will use 5 to the power of -4 for this example.

First, if the exponent is negative, then you turn it into a fraction of $\frac{x}{1}$.

Then you put the denominator on the bottom, therefor making the exponent positive (if the negative was originally on the bottom, you move it to the top).

Then you find out what the product of the power is and put that underneath a 1, in this case $\frac{1}{625}$

## Week 1 – Math 10

This week, I learned how to find prime factors using prime factorization. Prime factors can be used to find all the numbers factors (not just prime), if it is a perfect square or cube, and even its common multiples with other numbers.

You can find prime factors by following these steps (picture below), I will use the number 96 as an example.

Start by finding the lowest number that it can divide into and put it beside the number, in this case, the 2 is put beside the 96.

Under it, write the quotient of the number (in this case 48), and repeat what you just did. In this case it will divide into 2 three more times, so we will skip them and jump to when it can’t divide into 2.

Now it has become the number 3, which can’t be divided into 2 as a whole number. Plus, it is also a prime number, so it can only be divided by itself and one, so I will put 3 beside it, to turn it into 1.

After you reach 1, you stop.

Then you have all of its prime factors. You can multiply any and all of these together to find all of its factors. Because there are 5 2’s, you can simplify it by turning it into $2^5\cdot3$