This week in precalc we learned about sine and cosine law and when to use them. Sine law is used when you have an angle with a number across from it, then another number somewhere else on the triangle. Cosine law is used the rest of the time. Sine law has 2 different equations consisting of 3 fractions, the equations are either for finding a side or an angle. Then cosine law has 6 different equations in total, 3 of which are for finding a side and the other three are for finding the angle.
Here is an example of sine law.
Then here is an example of cosine law.
This week in PreCalc 11 we learned about adding and subtracting rational expressions with binomial and trinomial denominators. So the first step in any adding or subtracting of expressions, you need to simplify the whole equation, ex.
next with fractions, you need to find a common denominator then you can continue with the solving, ex.
Then from there you have to simplify it the most simple form.
Then for subtracting you just have to do the same but obviously subtract.
This week in PreCalc 11 we learned about multiplying and dividing rational expressions. First step in any equation is to simplify it if possible, ex:
After you can then figure out what x and sometimes y can’t be by looking at the denominator and if x can make the denominator 0, then those numbers can’t be x, ex:
After you state what x and y can’t be you then eliminate everything you can and then you have an answer.
Then for dividing you just have to state the restrictions for both the numerator and the denominator of the fraction after the divide signal and also under the one on the left of the divide signal. Then multiply the reciprocal of it.
This week in PreCalc 11 we learned about graphing the absolute value of a linear and quadratic function and the reciprocal of them. I will be focusing on the reciprocal form of linear equations, the first thing you do for it is graph the parent function. Next I would find the invariant points, then find the asymptotes, then draw the hyperbola’s.
Then you would find the invariant points by using 1 and -1 the look along the x line and find where it hit’s the parent line then that’s your invariant points. Ex: the green and blue lines represent where they are.
Then we have to find the x and y asymptotes, most of the time the x intercept is the y asymptote and then 0 is the x asymptote. Ex: the blue line represents the y asymptote and the green line represents the x asymptote.
Then lastly we just have to draw the hyperbola’s by using those lines as a guideline. Ex:
This week we looked at solving absolute value equations. It’s the same as last chapter but with the absolute value signs it changes it so the entire graph is positive.
Example of a linear equation
If you replace y with 9 perhaps, then you can find the x values
Then we can also do this with a quadratic equation:
Other than graphing it you can find the x values by solving if y was 6:
This week we dived more into graphing by graphing quadratic inequalities in two variables. It’s basically the same thing as chp. 4 but we have to find out what side of the parabola the answers would come from. You do that by replacing x and y with numbers that aren’t on the line, (0,0) is the easiest so use that the most.
Semingly I didn’t learn anything new this week, I did forget most about how to do sequences and series. But after studying I remembered how to find or how to find
But the one thing I had troubles with was finding when i am givin but after figuring it out I found it pretty easy because all you have to do is find out how many numbers are in between 4 and 10 and then the rest is easy.
This week in PreCalc 11 we learned how to take a word problem that looks like this, two number have a difference of 14, the product of those two numbers is the minimum, and we are able to find those two numbers.
We can do this taking a-b=14 and a*b=Minimum then isolating a in the subtraction equation the replacing a in the multiplication equation and then solve from there.
This week in PreCalc 11 we learned about analyzing quadratic functions of the form . We learned how to find everything that we need to using this equation.
To find the vertex you need to do the same thing as before, you need to look inside the brackets and take that number for the x-axis then use the end number and use that for the y-axis. Then with the vertex you can find the axis of symmetry, then with the coefficient of x, you can find if it’s a minimum or maximum, if it opens up or down. You can find what it’s congruent to, as well as the intercepts and the Domain and Range.
This week we looked a the discriminant and how to find how many roots there will be and what kind of root it will be.
You would need to use the equation -4ac.
If the discriminant is above 0 then it will have 2 roots and be considered a distinct root, a real root and a rational/irrational root. If the discriminant is equal to 0 then it will have 1 root and will be considered as a equal root and a real root. If the discriminant is below zero then it will have 0 roots and will be considered to have no roots.