Re: Sin Cos Tan, why not Sin Sec Tan?
From: |-|erc (gotch_at_beauty.com)
Date: 07/15/04
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Date: Thu, 15 Jul 2004 07:25:37 GMT
"Cassandra Thompson" <cass.harley@bigpond.com> wrote
> |-|erc wrote:
>
> > "Cassandra Thompson" <cass.harley@bigpond.com> wrote
> >
> >>Sin@ = O/H
> >>Cos@ = A/H
> >
> >
> > These 2 are grouped together because they divide by the longest
> > side on the triangle and are both <=1.
> >
> > But Tan is useful for the simplest of geometrical calculations
> > so it became a 3some.
> >
> >
> >>Tan@ = O/A
> >
> >
> > Either Tan or Sin&Cos can be taught 1st, IMO.
> >
> > Herc
> >
> >
> >
> NB.
>
> I should add that you have cleared it up somewhat.
>
> You are in effect saying (regardless of my slight confusion as to why
> sin/cos is better to teach first then sec/csc) that we are teaching the
> students:
> (sin/cos) and (tan)
>
> as opposed to
> (sin, cos, tan)
>
> Is this correct?
Yes.
This is probably the main underpinning of the preference.
Results 1 - 10 of about 1,820 for "sin wave".
but there are many others some mentioned already. In virtually
any engineering or computing field you will use sin routinely.
Also d/dx sin(x) = cos(x)
We did months on just Tan in year 10, and in year 11 we did a unit on circles
with mostly just sin and cos and different definitions that sin@ = y and cos@ = x.
(on the unit circle).
Sin describes vibrations, propogation, directions, .. it applies to the real world.
To use the inverse trig functions you're probably working things out backwards.
Like www.searchsky.com it plots the stars locations onto the screen.
"Inverse functions for an inverse application!!" I just checked the code has about
100 sin and 10 asin. This is the section to approximate the moon position.
I mean reciprocal not inverse.. but anyway same argument.
L1 = trange(280.466 + 36000.8 * t);
M1 = trange(357.529+35999*t - 0.0001536* t*t + t*t*t/24490000);
C1 = (1.915 - 0.004817* t - 0.000014* t * t)* dsin(M1);
C1 = C1 + (0.01999 - 0.000101 * t)* dsin(2*M1);
C1 = C1 + 0.00029 * dsin(3*M1);
V1 = M1 + C1;
Ec1 = 0.01671 - 0.00004204 * t - 0.0000001236 * t*t;
R1 = 0.99972 / (1 + Ec1 * dcos(V1));
Th1 = L1 + C1;
Om1 = trange(125.04 - 1934.1 * t);
Lam1 = Th1 - 0.00569 - 0.00478 * dsin(Om1);
Obl = (84381.448 - 46.815 * t)/3600;
Ra1 = datan2(dsin(Th1) * dcos(Obl) - dtan(0)* dsin(Obl), dcos(Th1));
Dec1 = dasin(dsin(0)* dcos(Obl) + dcos(0)*dsin(Obl)*dsin(Th1));
F = trange(93.2721 + 483202 * t - 0.003403 * t* t - t * t * t/3526000);
L2 = trange(218.316 + 481268 * t);
Om2 = trange(125.045 - 1934.14 * t + 0.002071 * t * t + t * t * t/450000);
M2 = trange(134.963 + 477199 * t + 0.008997 * t * t + t * t * t/69700);
D = trange(297.85 + 445267 * t - 0.00163 * t * t + t * t * t/545900);
D2 = 2*D;
R2 = 1 + (-20954 * dcos(M2) - 3699 * dcos(D2 - M2) - 2956 * dcos(D2)) / 385000;
R3 = (R2 / R1) / 379.168831168831;
Bm = 5.128 * dsin(F) + 0.2806 * dsin(M2 + F);
Bm = Bm + 0.2777 * dsin(M2 - F) + 0.1732 * dsin(D2 - F);
Lm = 6.289 * dsin(M2) + 1.274 * dsin(D2 -M2) + 0.6583 * dsin(D2);
Lm = Lm + 0.2136 * dsin(2*M2) - 0.1851 * dsin(M1) - 0.1143 * dsin(2 * F);
Lm = Lm +0.0588 * dsin(D2 - 2*M2)
Lm = Lm + 0.0572* dsin(D2 - M1 - M2) + 0.0533* dsin(D2 + M2);
Lm = Lm + L2;
Ra2 = datan2(dsin(Lm) * dcos(Obl) - dtan(Bm)* dsin(Obl), dcos(Lm));
Dec2 = dasin(dsin(Bm)* dcos(Obl) + dcos(Bm)*dsin(Obl)*dsin(Lm));
HLm = trange(Lam1 + 180 + (180/Math.PI) * R3 * dcos(Bm) * dsin(Lam1 - Lm));
HBm = R3 * Bm;
I = 1.54242;
W = Lm - Om2;
Y = dcos(W) * dcos(Bm);
X = dsin(W) * dcos(Bm) * dcos(I) - dsin(Bm) * dsin(I);
A = datan2(X, Y);
EL = A - F;
EB = dasin(-dsin(W) * dcos(Bm) * dsin(I) - dsin(Bm) * dcos(I));
W = trange(HLm - Om2);
Y = dcos(W) * dcos(HBm);
X = dsin(W) * dcos(HBm) * dcos(I) - dsin(HBm) * dsin(I);
A = datan2(X, Y);
SL = trange(A - F);
SB = dasin(-dsin(W) * dcos(HBm) * dsin(I) - dsin(HBm) * dcos(I));
not too complicated to be accurate to 10,000 years!
Herc
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