U know how sine = opposite / hypotenuse? How does the sine function on a calculator work without knowing the side lengths of the triangle?
Sin= opp/hyp only works on RIGHT triangles......if you checked several right triangles with various length sides BUT THE SAME angles, you would find that opp/hyp will always equal the same number for a given angle.......then they just built that number into the calculator software/firmware/hardware/algorithm.....
~jc
The calculator converts "degrees" into "radians" and then it uses a very sophisticated technique called
CORDIC (for COordinate Rotation DIgital Computer), also known as Volder's algorithm, which is a simple and efficient algorithm to calculate hyperbolic and trigonometric functions, typically converging with one digit (or bit) per iteration. Some calculators use the infinite Taylor series for "sine", which goes like this: sin=x-x^3/3!+x^5/5!- x^7/7! + x^9/9!........, which converges to Sine very rapidly.
Yikes ! That is probably more than you wnated to know (or I remember from advanced applied math years ago) I'll believe the algorithm Guest#2 wrote about is what the hardware executes to determine the value for sin.
The important thing to remember is the Sides of the RIght triangle determine the angle between them....that angle will always have the same value for sine cos etc.
......and the 'calculator' just 'calculates' the value for this angle.....
Thanx Guest #2......wish I remembered that stuff !
