05 · The bill

Ascent

You keep the launch site’s latitude as a minimum inclination unless you burn sideways. East picks up spin. Polar throws the coupon away on purpose.

In English

Launch due east from the equator and you keep 465 m/s of free speed and a 0° inclination. Launch from Cape and the cheapest orbit is 28.5°. Polar maps want Vandenberg, not a dogleg from Florida.

Try this: Cape, azimuth 90°. Then swing toward 0°. Inclination climbs; the rotation coupon shrinks.
Keep this: Inclination ≥ latitude unless you pay. East is a coupon.

Lab · go east, stay above your latitude

A rocket keeps the launch site’s latitude as a minimum inclination unless it burns sideways. Sideways is expensive. East picks up Earth spin. Polar (Vandenberg south) throws that coupon away on purpose.

Azimuth 90° (90 is due east)

Inclination: 28.5°
Rotation boost: +409 m/s

You cannot reach orbits below ~28.5° from here without a plane change.

Spherical-Earth rule: cos i = cos φ sin Az. Due east from latitude φ gives i = φ. Doglegs cost Δv. Range-safety corridors constrain Az more than textbooks admit.

Sun-synchronous wants ~98°. That is why weather sats leave Vandenberg, not the Cape. GEO wants 0°, which is why Kourou is a better pad than Baikonur for that job.