Trigonometry Methods

Remember: There is more than 1 way to do everything.  

This is only one way.  Whatever works for you. 


Quadratic formula

1.  Get the quadratic equation in standard form (ax2+bx+c=0).

2.  displaymath108  

3.  Substitute for a,b, and c.

4.  seperate into 2 equations (+ and -)

Roots of a quadratic equation

1.  Get everything to 1 side (set =0)

2.  Factor

3.  Set each factor=0

4.  Solve each equation for x.

5.  Check your solutions.

Factoring trinomial when a is not =1 (Lesson 5)

1-4.  Same as when a=1

5.  Rewrite original equation as ax2+first(x)+second(x)+c

6.  Pull out common factors of first two terms and last two terms.

7.  Answer = (shared terms)(remaining terms.

Ex: 3x2-x-4

3(-4)=-12 -12=-1(12), 1(-12), -2(6), 2(-6), 3(-4), -3(4)





Factoring trinomial with a=1 (ax2+bx+c) (Lesson 5)

1.  Multiply a(c)

2.  Find all factor pairs of that number. (call them first and second)

3.  Choose the pair whose SUM is b.

4.  Factors are (x+first)(x+second) (minus if negative)

Ex:  x2-5x-14

1(-14)=-14 -14=-1(14), 1(-14), -2(7), or 2(-7) 


(x+2)(x-7) = answer 

Common Factors: (Lesson 4)

1.  Write each part expanded to lowest form (ex 4x2=2*2*x*x) 

2.  Everything that is shared circle (or underline)

3.  Write Shared Terms(Leftover Terms) 

Ex.  12x2y+18xy2

2*2*3*x*x*y + 2*3*3*x*y 

2*3*x*y(2*x+3*y) or 6xy(2x+3y) 

 Difference of Perfect Squares: (Lesson 4)

1.  Take the square root of each part.

2.  Answer is (square root of first + square root of second)(Square root of first - square root of second)

Ex.  x2-y2 Factors to: (x+y)(x-y) 


Solving Absolute Value Inequalities: (Lesson 3)

1-5.  Same as solving an equation (don't worry about sign yet)

6.  If original question is < then "Thumbs Down."  

Your solution will look like smaller number < x < bigger number

7.  If original question is > then "Thumbs Up."   

Your solution will look like  x  AND

x> bigger number 


Solving Absolute Value Equations: (Lesson 2)

1.  Get the absolute value by itself on one side

2.  Once the absolute value is by itself, make sure it equals a positive number otherwise there are no solutions.

3.  Set up 2 equations, 1 where it equals what it equals, the other where it equals the negative.   ONLY negate the right side.

4.  Solve for each equations using inverse operations. (addition<-->subtraction, multiplication<-->division)

5.  There will be 2 solutions (unless = 0)