CPR: Circles, Pi, and Radians!

Hey guys! We've just started the Circular Functions unit, so I'll be talking about Pi, and converting degrees to radians and vice versa.

Pi

What do you think about when you think about Pi?

• APPLE PIE!
• 3.14 
• 180°
• Circumference (2πr)

Before this lesson, if someone were to ask you if π = 3.14 were exactly the same, what would you have said? Yes.

But we know better now, right? We now know that π is an exact value and 3.14 is and approximate value.

If π is 180°, then we should all agree that 360° is 2π, 90° is π/2 and 270° is 3π/2.

When an angle is positive, the rotation of the ray is counterclockwise, and when the angle is negative, the rotation of the ray is clockwise.

Converting Degrees to Radians

The formula for converting degrees to radians is   π   .

                                                                              180°

For example: Convert 90° radians.

90° ·   π  

         180°

=   π    = 1.570796327 = 1.57

 2                                   

*Unless otherwise stated, round your answer up to 3 decimals.*

Now, to convert radians to degrees, you can use the formula 180° .

                                                                                                    π

For example: Convert 3.14 to degrees.

3.14 ·180° 

                                                                                     π

= 179.91°

REMEMBER: π is not the same as 3.14 because π is an exact value and 3.14 is an approximate value.

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This is JP if you can't tell :D

Multiplicity of a Musical Note. I meant a Zero.

Multiplicity of A Zero

Hello fellow classmates, Kerwin here. While I had so much fun in the jazz festival at Brandon, all things must come to an end. Today, I will be summarizing about the multiplicity of a zero in a polynomial. Time to get back to work...

"Multiplicity" refers to the number of times that its associated factor appears in a polynomial function. The zeros of any given polynomial function, y = f(x), are "in tune" with the x-intercepts of the graph and also correlates with the roots of the equation, 
f(x) = 0. 

For example: The polynomial (x – 7)²  (x + 6) has two identical zeros at x = 7 and a third zero at x = -2. (x – 7)(x – 7)(x + 6) are the roots of the equation. The graph shows:

Blue line passes through -6 ONCE

Blue line passes through 7 TWICE

Considering the graph above, the sign of the function changes at x = -6 but the sign of the function does not change at x = 7. Polynomial functions changes signs depending whether the degree of the function (odd or even). The graph above shows that the function changes sign at the x-intercept that corresponds with an odd multiplicity, where the graph crosses over the
x - axis at the intercept x = -6. The function does not change its sign at x-intercepts of even multiplicity. The graph touches the x-axis but does not intercept the line.

Another example: y = (x + 6)²(x – 7)² 

Blue line passes through -6 and 7 TWICE

In this graph, both zeros are at even multiplicity. The function did not change sign at the x-intercepts. The graph line only touches the x-axis but does not crosses it. Those parabolas looks like mountains, reminds me of the ones at Banff. Oh Banff...

Thank you for taking time to read my section of the vlog!
The next person to do another topic is...

(Insert picture of Janina here)

Integral Zero Theorem

Integral Zero Theorem by Michael.

Inverses of Quadratic Relations

Inverses of Quadratic Relations

Hey guys! Since Gurnoor takes forever to write the blog post he asked me to do it instead. I'll be talking about Inverses of Quadratic Relations.

There are 4 easy steps to find the Inverse of a Quadratic Relation:

1. Replace f(x) with y.
2. Switch x and y.
3. Solve for y.
4. Replace y with f-1(x)

Example: Algebraically find the inverse of the quadratic whose equation is: 

1) Switch x and y.

x = 2(y - 2)^2 + 3

2)Solve for y.

x-3 = 2(y - 2)^2

(x-3)/2 = (y-2)^2

sqrt[ (x - 3)/2 ] = y-2

The inverse of the quadratic is:{ f(x)= 2 - sqrt[ (x - 3)/2 ]

                                                                  AND

                                                       f-1(x) = 2 + sqrt[ (x - 3)/2 ] }

Graphed it would look like this: 

Horizontal line test

• The horizontal line test is used to determine if a function has an inverse that is also a function. 
• If a horizontal line intersects two or more places the inverse of the function is not a function.

Example: 

• This function fails the horizontal line test so its inverse is not a function

Example 2: 

• This function passes the horizontal line test meaning its inverse is a function.

Hope you guys enjoyed reading.

- SUKH

I choose:

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 I CHOOSE THIS GUY:

nice pic 22g.......

kaimzzzzzzzz broooo...................

sirrah 22g.........
aha swagg jatt da.........