This week in math, we learned how to find the rotational angles of a reference angle in each quadrant. First, the reference angle always come off of the x axis.
Example: refθ=30
First, label each reference angle.
Next, label each rotational angle.
Finally, find the rotational angles.
q1= 30
q2= 150
q3= 240
q4= 330
This week in math, we started our trigonometry unit. We learned what co terminal angles were. Co terminal means that the angles given would end up in the same spot.
Example:
180 degrees and -180 degrees. This would be a straight line.
Example:
270 degrees and -90 degrees.
We can tell if they add together to equal 360 degrees. One will be negative or more that 360 degrees.
Example 270 and -450. You would have to do a full loop first to find the position of -450.
This week in math, we learned how we can solve fractional equations using multiple different methods. The first method included cross multiplying. The other one included putting all the numbers over the same denominator.
Example:
Cross multiply
First, you collect the like terms to one side.
Then, simplify and cross multiply.
x=3
Like denominators
First, you put everything over the same denominator.
Then, collect like terms.
Next, multiply both sides by the denominator.
9=3x
Lastly, divide both sides by the coefficient.
x=3
Knowing that there are more than just one way to solve the same problem allows us to be able to solve in the most efficient way depending on the person. It allows us to have flexibility and also be able to solve using which way might be easier for the specific question.
This week in math, we learned how to simplify rational expressions.
Example:
First we need to see if there are any numbers that we can pull out of the expressions. Here, we pull out 4 from the top and 2 from the bottom.
Next, we factor the expressions.
Then, we cancel out any similarities. Here, we canceled out (x+3) from the top and bottom. We also simplify 4 over 2 to 2 over. 1
And now we have our answer!
This week, we learned how to find an equation of a function using the vertex and one point on the line. We then were about to put the equation into standard form.
Example 1:
Vertex= (3,-4)
Point= (4,1)
y=a(x-3)^2-4
*note: the vertex is put into the equation The x value, 3 is made negative and put into the equation with the 4 stays negative.
Next, input the point we were given into the x and y spots in the equation, then solve for a.
(1)=a(4-3)^2-4
1=a-4
5=a
Then take your a value and complete the equation.
y=5(x-3)^2-4
Then to put it into general form, we must expand the equation.
y=5(x-3)(x-3)-4
y=(5x-15)(x-3)-4
y=5x^2-15x-15x+45-4
y=5x^2-30x+41
Example 2:
Vertex=(7,-6)
Point= (9,-4)
y=a(x-7)^2-6
-4=a(9-7)^2-6
-4=a4-6
2=a4
1/2=a
y=1/2(x-7)^2-6
=1/2(x-7)(x-7)-6
=(1/2x-7/2)(x/1-7/1)-6
=1/14x^2-7/2x-7/2x+49/2-6
=1/14x^2-14/2x-37/2
y=1/14x^2-7x-37/2
This week in math, I learned how to write an inequality in interval notation. Interval notation is a notation of the x intercepts of an inequality.
Example: x^2 + x – 6<0
(x+3)(x-2)<0
x1=-3
x2=2
-3<x<2
Interval notation: (-3,2)
Example: x^2+9x+8≤0
(x+8)(x+1)≤0
x1=-8
x2=-1
-8≤x≤-1
Interval notation: [-8,-1]
Square brackets are for “greater than/less than or equal to“, round brackets are for “less than/greater than.”