Trig Mid Term
Terms
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copy deck
- Closure Property
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Addition: a + b is a real number.
Mult: ab is a real number. - Communtative
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Add: a + b= b + a
Mult: ab= ba - Associative
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Add: (a+b)+c = a+(b+c)
Mult: (ab)c=a(bc) - Identity
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Add: a+0=a, 0+a=a
Mult: a*1=a, 1*a=a - Inverse
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Add: a +(-a)=0
Mult: a*(1/a)=1, a never = 0 - Distributive
- a(b=c)=ab+ac
- Order of Operations
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1. Do operations that occur within grouping symbols.
2. Evaluate powers.
3. Do multiplications and divisions left to right.
4. Do additiond and subtractions fromleft to right. - Distance Formula
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d=rt
distance equals rate times time. - Simple Interest
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I=Prt
Interest equals principal rate times time - Temperature
- F= 9/5C+ 32
- Area of Triangle
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A=1/2bh
Area equals 1/2 base times height - Area of Rectangle
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A=lw
Area equals length times width - Perimeter of Rectangle
- P= 2l+2w
- Area of Trapezoid
- A= 1/2(b1+b2)h
- Area of Circle
- A= pie R squared
- Circumference of Circle
- C=2 pie R
- Slope
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M=(y2-y1)/ (x2-x1)
rise over run
Classification of lines by slope:
parallel: same
perpendicular: reciprocal
Horizontal: 0
Vertical: Undefined - Slope Intercept Form
- y= mx+b
- Point Slope Form
- y-y1= m(x-x2)
- Two Points
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m= (y2-y1)/ (x2-x1)
Then y-y2= m(x-x2) - Area of a Triangle Matrix
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Area= +- x1 y1 1
x2 y2 1
x3 y3 1
x1-3 and y1-3 given. - Cramer's Rule 2X2 matrix
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2X2:
ax+by= e
cx+dy= f
det not equal 0, x= e b
f d
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det a
y= a e
c f
___
det a - Cramer's Rule 3X3
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ax+by+cz= j
dx+ey+fz= k
gX+hy+iz= l
X= j b c
k e f
l h i
over det a
y= a j c
d k f
g l i
over det a
z= a b j
d e k
g h l
over det a - Quadratic Functions
- y= ax^2+bx+c
- X coordinate of vertex
- -b/ 2a
- Axis of symmetry
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Vertical line
x= -b/2a - Vertex Form of Quadratic Functions
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y=a(x-h)^2+k
vetex= (h,k)
Axis of symmetry x=h - Intercept Form of Quadratic
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y= a(x-p)(x-q)
X intercepts= p and q
Axis of symm: halfway between
(p,0) and (q,0) - Complex Numbers
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Square root of -r = i square root of r
i^2= -1
(i-/ r)^2= -r - Completing the square
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ax^2+bx+c=0
1. Move constant to the right side of the equation
2. take 1/2 of b, square it, and add to both sides of the equation.
3. rewrite left side as binomial squared and simplify right side.
4. take square root of both sides.
5. solve for x and simplify.