### 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=3x

^{2}+ 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: }θ

_{r}= 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 = 5sinθtanθ + 2tanθ

0 = 5sinθtanθ + 2tanθ

*Then, factor out tanθ.*

0 = tanθ (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:

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

6:55 PM

Nice one Carla...

Magnificent post...

1:08 AM

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