How do you a graph trig functions?

Answer 1

The basic equation is of general form y = R(x) where (here) R is the Sine, Cosine or Tangent of x, and consequently the Sine and Cosine curves plot oppositely from +1 via 0 to -1 (minus 1) over 180º. The y-values of the Tangent curve goes cyclically from 0 to infinity as x goes from 0º to 90º: it looks odd at first, and you might even think you've gone wrong!

Plot in the usual way: left-hand column or top row for suitable increments of x = [angle in degrees], neighbouring columns or rows below for the corresponding ratio values. To get the best out of it, plot 0º to 360º, to give a whole Sine Wave cycle - it and the Circle to which it can be related geometrically, being perhaps the 2 most important curves in Nature!

Answer 2

There is no simple solution. You need to select a span of 2pi radians (360 degrees) for sine, cosine and their reciprocals, or pi radians (180 deg) for tan and cotangent. Select a set of values within these domains and use a calculator or table to find the values of the trigonometric ratio and then plot them. Beyond the selected values the functions will repeat itself.

Note that there are some values where all the ratios except sine and cosine are asymptotic and your calculator will indicate an error.