Angular and Linear Momentum; Graphing Sin and Cosign

Arc Length

s=rθ

Area of a Sector of a Circle

½ r²θ

Spinning

Angular Motion

Out in a line (Velocity)

Linear Motion

V

linear Velocity

w

Angular Velocity

v =

r(w)

w =

θ/t

For graphing cosine

f(θ) = a cos (bθ)

For graphing sin

f (θ) = a sin (bθ)

Amplitude

Distance between the midline and the max/min

Period Cycle

2π/b

Frequency

b/2π

Midline

y=k

Period of tan

π/b

To get the asymptotes for tan and sec

θ = π/2 + kπ

Pattern for Sine

Center, top, Center bottom, Center

Maximum for Sin

y = midline + amplitude

Minimum for Sin

y = midline - amplitude

For phase shifts of sin

Set θ = 0

Pattern for Cosine

Max, Midline, Min, Midline, Max

Maximum for Cosine

y = midline + amplitude

Minimum for Cosine

y = midline - amplitude

Phase shifts for Tan

Set θ = 0

For phase shifts of Cosine

Set θ = 0

Pattern for Tangent

Left, Center, Right

Left-point equation for Tan

y = vertical shift - vertical stretch

Center-point equation for Tan

y=vertical shift

Right-point equation for Tan

y=vertical shift + vertical stretch

Pattern for Cot

Left, Center, Right

To find the asymptotes for cot and csc

θ = kπ

Left-point equation for cot

y=vertical shift + vertical stretch

Center-point equation for cot

y=vertical shift

Right-point equation for cot

y=vertical shift - vertical stretch

For a pulley system

Linear speeds are equal

For a coaxial system

The angular speed is equal