1.7 precalc

Limaçon type (a + b cosθ or sinθ):

• a/b < 1 → inner loop

• a/b = 1 → cardioid

• 1 < a/b < 2 → dimple

• a/b ≥ 2 → convex

Rose curves (a cos nθ or sin nθ):

• n odd → n petals

• n even → 2n petals

Circles:

• r = constant → center at pole

• r = a cosθ → x-axis, r = a sinθ → y-axis

Lemniscate:

• r² = a² cos 2θ or sin 2θ → figure 8

Line:

• r=n/sin0

• r=n/cos0

θ = π/2

• (-r,-θ)

Polar Axis

• (r,-θ)

Pole

• (-r,θ)

Polar Form of Complex Number

Polar Form of a Complex Number

• z=r(cosθ+isinθ)

• r=∣z∣= sqrt(a²+b²)