Proportions: Rational Trigonometry To Un... | Divine

: The rational equivalent of the Cosine Law (using "cross"

(Q1+Q2−Q3)2=4Q1Q2(1−s3)open paren cap Q sub 1 plus cap Q sub 2 minus cap Q sub 3 close paren squared equals 4 cap Q sub 1 cap Q sub 2 open paren 1 minus s sub 3 close paren Why This Matters : You never need to use a calculator for 2the square root of 2 end-root . All results are exact fractions. Divine Proportions: Rational Trigonometry to Un...

s=QoppositeQhypotenuses equals the fraction with numerator cap Q sub o p p o s i t e end-sub and denominator cap Q sub h y p o t e n u s e end-sub end-fraction The spread ranges from indicates parallel lines and indicates perpendicular lines. 3. Apply the Main Laws : The rational equivalent of the Cosine Law

with purely algebraic concepts. By avoiding irrational numbers and infinite series, it allows for exact calculations over any field, not just the real numbers. 1. Replace distance with quadrance not just the real numbers.

: Computers are much faster at adding and multiplying than calculating trigonometric series.

s1Q1=s2Q2=s3Q3the fraction with numerator s sub 1 and denominator cap Q sub 1 end-fraction equals the fraction with numerator s sub 2 and denominator cap Q sub 2 end-fraction equals the fraction with numerator s sub 3 and denominator cap Q sub 3 end-fraction