Stephanie's Reflection

Limacon
r=a+b sin(theta)
r=a+b cos(theta)

Cardioid
a-b sin(theta)
r=a-b cos(theta)

Rose
r=a sin(n theta)
r=a cos (n theta)
n=how many petals

Archimedes Spiral
r=a theta+b

Logarithmic Spiral
r=a b^theta

Circle With Pole Center
r=c

Circle Intersecting Pole
r=a sin(theta)
r=a cos(theta)

1. Sine and Cosine Sum/Difference Formulas

• cos(alpha+/-beta)=cos alpha cos beta-/+sin alpha sin beta )
• sin(alpha+/- beta)=sin alpha cos beta +/-cos alpha sin beta
• sin x+sin y=2sin(x+y/2)cos(x-y/2)
• sin x-sin y=2cos(x+y/2)sin(x-y/2)
• cos x+cos y= 2cos(x+y/2)cos(x-y/2)
• cos x-cos y=-2sin(x+y/2)sin(x-y/2)

2. Tangent Sum/Difference Formulas

• tan(alpha+beta)=tan alpha+tan beta/1-tan alpha tan beta
• tan alpha-beta=tan alpha-tan beta/1+tan alpha tan beta

3. Double-Angle/Half-Angle Formulas
sin 2 alpha=2sin alpha cos alpha

• cos 2 alpha=cos^2 alpha-sin^2 alpha=1-2sin^2 alpha=2cos^2 alpha-1
• tan 2 alpha=2tan alpha/1-tan^2 alpha
• sin(alpha/2)=+/-sqrt(1-cos alpha/2) cos(alpha/2)= +- sqrt(1+cos alpha/2)
• tan(alpha/2)= +- sqrt(1-cos alpha/1+cos alpha)=sin alpha/1+cos alpha= 1-cos alpha/sin alpha

if you have a decimal, us the half-angle formulas for alpha and then multiply the decimal angle by two