identities

Pythagorean identities

1+cot*2=csc*2

1+ tan*2=sec*2

Sin*2+cos*2=1

Sin(x+y)

Sinxcosy+sinycosx

Cos(x+y)

Cosxcosy-sinxsiny

Tan(x+y)

Tanx+tany/1-tanxtany

Sin(2x)

2sinxcosx

Cos(2x)

(Cosx)*2-(sinx)*2

Tan(2x)

2tanx/1-tanx*2

Sin(x/2)

+ (1-cosx/2)*1/2

Cos(x/2)

+(1+cosx/2)*1/2

Tan(x/2)

1-cosx/sinx

Circle equation

(X-h)*2 + (y-k)*2 = r*2

Ellipse equation

(X-h)*2/(rx)*2 + (y-k)*2/(ry)*2 =1

Hyperbola equation

Opens left/right: (X-h)*2/(rx)*2 - (y-k)*2/(ry)*2 =1

Opens up/down: (y-k)*2/(ry)*2 - (x-h)*2/(rx)*2 =1

Parabola equation

Opens up/down: Y=a(x-h)*2+k

Opens left/right: x=a(y-k)*2+h

Polar conversions

X=rcosø

Y=rsinø

X*2+y*2=r*2

Tanø=y/x

Circle

r=2asinø centered at (a,π/2)

r=2acosø centered at (a,0)

Cardioid

Heart

r=a+acosø

r=a+asinø

Limacon

Heart with loop

r=a+bcosø

r=a+bsinø

Rose

Flower petals

r=acos(nø)

r=asin(nø)

If n is odd, rose has n leaves

If n is even, rose has 2n leaves

Lemniscate

Figure 8

r*2=a*2sin2ø

r*2=a*2cos2ø

IVT

since f(x) is continuous on [a,b] and f(a)<k<f(b), there exists at least one “c” on [a,b] such that f(c)=k

Continuous rules

1. F(k) is defined

2. Lim as x→k exists

3. Lim as x→k = f(k)