### December 2019 archive

This week in Precalc 11 I learned the Sine law. The golden rule when it comes to Sine law is ” You can only use this law if you have at least one angle and its corresponding angle”, if you don’t have an angle and its corresponding side then you can not use this law.The formula for the Sine law also differs whether you are finding an angle or a side. Today I will be going through how to use Sine law when you are finding a side.

If you are finding a side, the formula is :

If you are finding an angle then you just flip it:

Here is an example and the steps I would take when solving for a side using the Sine law:

This week in precalculas 11 we learned about special triangles. We use these special triangles when the angle is 30, 60, and 45 degrees. For these special triangles we will not have to use a triangle and they give us a more exact answer.

These are our special triangles:

This is an example and the steps I would take to solve for an angle:

A question I struggled with this week was:

I was doing alright until I was at the solving step:

As you can tell, I was conflicted about whether I should cancel the two out or not, and the answer is yes because they are opposites.The rule says you can but you have to put a negative one (-1) in the numerator.

This week in Precalculas I learned how to identify the Non- permissible values of a rational expression. A non – permissible value is a number that would cause the denominator to equal zero. An example on how to find one while simplifying or solving an expression is this:

This week in Precalculas 11  I learned how to graph an inequality. The main difference between inequalities and equations is that equations are equal to 0 and inequalities are not. An inequality can come in many forms and symbols that show the inequality. For example, there is the Greater than symbol >, Less than symbol <, Greater than or equal to symbol ≥, and the Less than or equal to symbol ≤. The symbols determine which part of the graph the answer will be on. If the symbol is equal to and has a line below then it means the point on the graph will be a filled in circle. If it is not equal to then it doesn’t include the point and the circle is not filled in. The other thing we learned this week is how to write answers in interval notation. This is where you use different brackets and symbols to determine what the answer is. For example, if you consider the fact that the lines don’t have domains or ranges and they go on forever if they don’t have a point it would be infinity  (∞), this is only if it’s moving to the right of the number line and is greater than 0. If the lines go on forever but are moving to the left of the number line and is less than 0, then it will be a negative infinity sign ( – ∞). Also when you write in interval notation if the number has a filled in circle and it is equal to then you would use a square bracket, [, ]. If the number is a non – filled circle and is not equal to, you would use round brackets (, ). We also use the round brackets when you are describing the line or parabola with ∞. An example of writing something in interval notation would be (-∞, 5]. Another key note is that if the x is on the smaller end of the symbol x<0 the area that we are focusing on is the inside part of the parabola. If it is the opposite and x>0 then the part we focus on is the outside of the parabola. Another important note is that whenever you are solving an inequality you must always flip the symbol when you divide by a negative.