I'm stuck on a math conundrum

[AppleDavidJeans]

Alright, so I'm writing programs on my calculator for my project here and I'm writing a program where you can calculate a satellite's periapsis and apopasis just by using a launcher's (with the satellite of course) final burnout altitude, velocity, and the velocity vector. I'm using this equation from Robert Braeunig's excellent Rocket and Space Technology page to write out the equation on my calculator. Here is the equation

( -C ± SQRT[ C² - 4 × (1 - C) × -sin²(Z) ]) / (2 × (1 - C))

where:

C = 2 × GM / (r1 × v1²)

r1 is distance from center of body being orbited.

v1 is velocity at burnout.

Z is the zenith angle, or angle between an imaginary vertical line extending from the center of the body being orbited and prograde vectors (not in terms of absolute value).

The real problem I am having is the term -sin²(Z). I've never seen a sine worded like that, but then again, I'm only in 10th grade Algebra II Honors. I'm trying to write the equation in an understandable form for my calculator. My calculator is a TI-84 Plus C Silver Edition.

[Chrisd857]

sin²(x) is just a stylistic shorthand for sin(x)² or sin(x) * sin(x)

[1greywind]

-sin^2(Z) = -1 * sin(Z) * sin(Z)

[TythosEternal]

sin^2(z) is just sin(z) * sin(z). Sometimes we place exponents after an operator but before it's arguments. This helps clarify, in theory, that we are raising the result of the operator by a power, and not the arguments themselves.

Edited October 6, 2014 by TythosEternal
Clarifying absence of minus