What is trigonometry (trig)?
Trigonometry is the study of triangles and the relationship of angles and sides in a triangle. Before even finding side lengths using trig, you need to label all the sides of the triangle. There are three special names for each side; there is hypotenuse, opposite, and the adjacent. The hypotenuse is the longest side and is always across from the right angle (90-degree angle). The opposite side is across from the reference angle. And the adjacent is the side beside the reference angle.
What are the ratios?
SINE RATIO = opposite (divide by) hypotenuse
COSINE RATIO = adjacent (divide by) hypotenuse
TANGENT RATIO = opposite (divide by) adjacent
An easy way to memorize these ratios is with the acronym SOH CAH TOA. Therefore is each of the ratios first letters into a big word.
For every trig equation : Ratio (REFERENCE ANGLE) = side 1/side 2
In this example, we need to see what ratio we will use, and from the process of elimination the ratio needed is SINE. Next, we use algebra to find the answer.
When simplifying an expression that includes exponents there are exponents laws that one could use to answer the question easier. The laws of exponents can be thought of just “tricks” or shortcuts that help us work with exponents in equations. Some of these laws for exponents are the Power Law, Multiplication Law, and Division Law. However, we are going to focus on just the division law.
The first thing to do when using the division law is to identify the same bases with exponents. If the bases are not the same, you can’t use the division law and won’t be able to simplify it any more. Next, you will subtract the exponents leaving you with one number with one exponent. To divide exponents (or powers) with the same base, subtract the exponents. The coefficients (if any) won’t be affected by the division law. As division is the opposite of multiplication, so it makes sense that because you add exponents when multiplying numbers with the same base, you subtract the exponents when dividing numbers with the same base.
If when you are subtracting the exponents and the result is a negative exponent then you will use the Negative law to further simplify the expression.
This week when I was doing a practice question to find the least common multiples when using numbers’ prime factorizations. I could not figure out why I kept on receiving with the wrong answer, no matter what. What I was doing wrong? I tried doing it over again but came up with the same results. Then after more explanation, I learned that I multiplied the common numbers of the prime factorization twice instead of the once I needed to do. I also now have a useful technique to find the least common multiples.
Firstly, what are the least common multiples? Least common multiples (LCM) are the smallest positive number that can be divisible by both of the numbers. The way to determine the LCM is to take all the prime numbers of one of the numbers and multiply by any additional factors in the other numbers. An easy way to find the common numbers in two prime factorizations for the LCM is to use a Venn diagram. You can take a Venn diagram and put the common numbers from both of the prime factorizations in the middle. After that, put the remaining numbers from their prime factorizations in the other two sides of the Venn diagram. Then multiply all the numbers together for the LCM.
Let’s do exemple: