This is a blog for my second semester pre-calculus 30s students. Have a blast!

Thursday, March 02, 2006

Quad./Trig. Equation

This is my first Scribe Post, so just bear with me and I apologize if you do not understand what I’m saying. I’m just not good at explaining things.

Today, the lesson was about Quad/Trig Equations. This lesson involves a lot of factoring. We did a recall about what a quadratic equation is.

  • A Quadratic Equation is an equation with the highest power, which is 2.
    • Example:
      • Y= X2
    • This could be a quadratic equation:
      • f(x) = sin2θ


Example:
Solve: y=3x2 + 2x - 1

  • First, try to see if it can be factored. In this case, it can be.

y= (3x-1) (x+1)

  • Then, change Y into a zero.

0=(3x-1) (x+1)

  • Then, let each factor equal to zero.

3x-1=0

-----------

x+1=0


  • Solve for x.

3x= -1

x=-1/3


------------

x= -1



In this next example, we'll do the exact same thing. Just imagine that the sinθs are the x variables.


  • Solve: 2sinθ - sinθ - 1.

y= (2sinθ + 1) (sinθ - 1)

0 = (2sinθ + 1) (sinθ - 1)


2sinθ = -1

-----------------

sinθ = 1

*But this time, we solve for angles, not just numbers.*

sinθ = -1/2


θ = -30
°

-----------------

sinθ = 1


θ = 90
°

*Since the angle is negative,
we have to find the related
angle in the 1st quadrant.*


θ
r = 30°

Q3:
θr = 180° + 30°

= 210
°

Q4: θ
r = 360° - 30°

= 330
°

Therefore, the angles are 90
° , 210° , 330° .

Here's another example:
  • Solve: 5sinθtanθ = -2tanθ

*First, we need to transpose the -2tanθ to the left.*


y = 5sin
θtanθ + 2tanθ

0 =
5sinθtanθ + 2tanθ

*Then, factor out tanθ.*


0 = tan
θ (5sinθ + 2)

tanθ = 0
°

θ = 0
°

*This is a special situation.

We need to find where tanθ
is 0 other than Q1. It is in
the 180 Quadrant and
360 Quadrant.*

θr = 180
°, 360°

-------------------

5sinθ = -2


θ = -2/5


θ = -23.6
°

θr = 23.6
°

Q3: θr = 180
° + 23.6°

= 203.6
°

Q4: θr = 360
° - 23.6°

= 336.4
°


Therefore, the angles are 0
°, 180°, 203.6°, 336.4°, 360°.





If i'm right, we have a test tomorrow. So, good luck to everybody! Before i forget, the next scribe is,
Albert!

2 Comments:

Blogger Mr. Malandrakis said...

Great scribe post Carla. The lesson was summarized superbly. Keep up the great work!

6:55 PM

 
Blogger miles_23 said...

Nice one Carla...
Magnificent post...

1:08 AM

 

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