Week 18 in precalc 11 

My top 5 things 

1. my first favorite thing in precalc 11 is the multiplying of the fractions because it felt so nice to just multiply across the equal sign. A question likeX                         3                           5 

   ______ + _______ = __________ 

   (x-2)                   x                           2 

   Is very satisfying to just multiply across

the second thing was learning about the quadratic formula and the discriminant. I enjoyed learning about this because it was some I’ve never learned before, and I was impressed on how it worked. This formula was also useful for physics, where this equation popped up.

The third thing I enjoyed the most was mixed and entire radicals because I always enjoyed how easy they were to do, and I also did well on that unit test. multiplying and adding them were also fun

Another thing I enjoyed was the exponent rule. I was already familiar with them from previous years, so it was nice to revisit them, and made for a good review.

The last thing I enjoyed was learning about the restrictions. I didn’t know you need them whenever you had variables on the bottom, so they were good to learn

This week in precalc 11 I learned about the sine rule.  

Lets say you are given this triangle, and you are looking for the top angle. The sine rule is  

sinA  sinB    sinC 

—- = —- = ——- 

a           b          c 

But you only need two of them to make it work, and you need at least 3 pieces of information. 

We can then label the sides and make an equation 

Sin21      SinB 

——- =  —— 

4              5 

We multiply the sin21 by 5, then divide by 4 to get 0.4479… 

And the last step is to inverse sin, then multiply by the previous answer. 

If done correctly, the angle will be 27 degrees. 

This week in precalc 11 i learned about the cast rule  

The cast rule show where each ratio is positive 

 you can you the phrase “All students take calculus” to remember where the ratio’s are positive

Let’s say your calculator gives you 82 degrees from cos 35 

One may think that because the calculator gives you one answer in quadrant 1, that is the only answer. However, you must be smarter than your calculator to realize it can also be in a different quadrant. 

Looking at the CAST rule, a positive 82 degrees can be also found in Q4 

Therefore, we can take the 360 and minus 82 to get an angle of 278 degrees. 

So, there can be more angles shown without your calculator that you need to be able to do

This week in precal 11 

This week in precal 11 I learned some terminology for angles in the trigonometry unit 

The first term I learned was quadrants. There are four quadrants in graph, and there are specific spots for each quadrant. 

Quadrent 1 is in the top right,  

Quadrent 2 is in the top left, 

Quadrent 3 is in the bottom left, 

Quadrent 4 is in the bottom right, 

Another term i learned was the rotation angle. 

It is the angle in the middle formed by rotating an initial arm with the terminal arm 

And another term I learned was standard position.  

It is the positive side of the angle. 

Looking back at the, we can take a guess that it is 135°  

However, there is also a negative 225° in the other way

These two angles are called Coterminal 

This week in precal 11  

This week in precalc, I learned how to solve rational equations  

Let’s say you are given  

X                         3                           5 

______ + _______ = __________ 

(x-2)                   x                           2 

The first step is to add the left side together 

We need to have a common denominator  

We can multiply the left by x, and the right by (x-2) with the top side and the bottom 

After multiplying, we have this 

X^2                 3x-6                        5 

______ + _______ = __________ 

          X(x-2)                                    2 

We can put the terms together 

X^2 + 3x-6                              5 

_____________ = __________ 

X(x-2)                                         2 

Now we can cross multiply 

5x(x-2) = 2(x^2+3x-6) 

5x^2-10x=2x^2+6x-12 

We can move the like terms 

3x^2-16x+12=0 

We can the put it in the quadratic formula 

And have an answer of  

This week in precal 11 I learned how to simplify Rational expressions 

Let’s say you are given an equation of  

(3x-4) 4 

—— + —— 

2 (x+3) 

The first step is to find a common denominator 

We can multiply the 2 and the (x+3) to get a denominator of 2(x+3) 

Once we have the denominator, we need to multiply the (3x-4) by (x+3), and the 4 by 2 

Once multiplied we have  

3x^2-4x+9x-12 +8 

________________ 

2(x+3) 

We can then combine the like terms to have 

3x^2+5x-4 

_________ 

2(x+3) 

That is the final simplified answer with the restrictions of X cannot be -3 

This week in precal 11, I learned how to graph inequalities in 2 variables 

Here is an example question  

Y < X^2 –5 

The first step is to graph the parabola first 

We know the parabola starts at –5 and has a stretch value of 1 

The < symbol indicates that it does not include values on the parabola, therefore the parabola will be dotted. 

The last step is to shade the parts with the answers.  

To find this out, you can choose a point to test.  

After graphing the inequality in desmos we can confirm that our steps were right.

This week in precal 11 

This week in precal 11 I learned how to solve some word questions applications of a parabola. 

Here is an example question. 

If the fencing around a rectangular school yard is 80 m, and the area is 225 m, and if the length is x-meters long, what is the width of the fencing?   

What we can do now is draw a picture and label the sides.  

We can now create an equation for the sides 

2x+2y=80

Now we isolate the y 

2y=80-2x 

Y=40-x 

So we know the length is x-meters long ,and the width is 40-x meters, we can multiply them together as we know the area is 225 meters 

X(40-x) = 200 

40x –X^2 =200 

Move the like terms around 

X^2-40x-200=0 

We can complete the square 

X^2-20x+400-400-225=0 

(x-20)^2=625 

If we square root both sides we will be left with 

x-20=25 

We can isolate the x 

X=45 

We can put 45 back in the equation to find y 

Y=5