## Pre-Calc 11 Week #17

This week in PreCalc we started our trigonometry unit, while practicing what we know from previous years we slowly added in new things such as the sine law, this is something completely new that we haven’t done in previous years. The sine law is the following, a/sin A = b/sin B =c/sin C with the lowercase letters being the measurements of each sides and the uppercase letters that happen to be multiplied by sign being the angle for each letter respectively.

If there is a missing angle and not a missing side which is what the sine law is mainly for, you flip it to sin A/a = sin B/b = Sin C/c and it can work to find the missing angle as well. When using the sine law there is 3 equations to start with but once inputting values you only use 2 equations, leaving 1 variable in the full equation.

The sine law is used for triangles with a missing angle or side that aren’t right triangles and have an angle more than 90 degrees

Here is an example of how to use the sine law to find a missing angle

## Pre-Calc 11 Week #16

This week in PreCalc 11 we learned how to solve rational equations where fractions with binomial or trinomial numerators or denominators are multiplied or divided by eachother or on other sides of the equal sign. There are two main ways to solve these rational equations, 1 is by cross multiplying which is done when its 2 fractions on opposite sides of the equal sign and the other is to multiply for common denominators which is usually done when there are multiple fractions on one or both sides of the equal sign.

When dividing you flip the fraction that is dividing into and change the division sign to a multiplication sign.

Example,

## Pre-Calc 11 Week #15

This week in PreCalc 11 we learned about adding and subtracting rational expressions that have binomial and trinomial denominators. So the first step in any adding or subtracting of expressions, you need to simplify the whole equation by finding common factors in the numerator or denominators.

Example,

Next we need to find a common denominator so we can add just like a normal fraction

Then you just have to simplify it further by taking the brackets out and adding/substracting respectively

## Pre-Calc 11 Week #14

This week we learned about the difference between reciprocal function graph and absolute value graphs and how to graph each one.

For absolute value graphs it is graphs that reflect off the x axis/intercepts of the line to create a reflection of the parent function as in an absolute value equation we can’t get a negative, so in the graph we can’t go into the negative zone.

In a reciprocal function graph we focus on the invariant points in the parent function to create a new line that avoids the asymptotes on the x and y axis, y is usually 0 so it’s usually the x axis that we want to focus on. We use the middle of the invariant points to create the x asymptote.

Example of absolute value graph

Example of reciprocal function graph

## Pre-Calc 11 Week # 13

This week we continues graphing linear/quadratic equations but this week practiced on finding the reciprocal of the equation and how it looks like when graphed.

To find the reciprocal of the equation we first have to graph the parent function, then we find our invariant points by finding the x value that corresponds with y=1 and y=-1

With these x values we can draw our hyperbolas and answer what the x value is.

Ex