How can you get the sine and cosine of a given angle?

Answer 1

I generally use (in order of preference):

1. a scientific calculator and the [SIN] and [COS] buttons;
2. a spreadsheet and the =SIN() and =COS() functions;
3. a slide rule and the SIN and COS scales;
4. SIN and COSINE tables (though some of my table books only have a SINE table (for these the COSINE of an angle is the same as the SIN of 90o ± the angle) and only for 0o - 90o: other angles are worked out by converting them to this range dependant upon which quadrant they are in, which can also affect the sign of the result); or
5. convert the angle to radians (angle_in_radians = angle_in_degrees x π/180o) and then use enough terms of the appropriate formula get the required accuracy:

sin(x) = x - 1/3! x3 + 1/5! x5 - 1/7! x7 + ... + 1/(2r+1)! x2r+1 (-1)r + ...

cos(x) = 1 - 1/2! x2 + 1/4! x4 - 1/6! x6 + ... + 1/(2r)! x2r (-1)r + ...

for r = 0, 1, 2, ...