Question

Evaluate the following sin 30°- cos 30°?

Answer 1

No trick on this one, just another sad 30/60/90 trig question:

`sin 30^circ - cos 30^circ = 1/2 - sqrt{3}/2 = 1/2(1-sqrt{3})`

Explanation:

The first time we see the 30/60/90 triangle we can recognize it's half an equilateral triangle and do the `(s/2)^2 + h^2 = s^2` thing to work out the trig ratios. The next hundred thousand times we just remember the results and spit them back out.

Trig mostly uses two triangles, 30/60/90 and 45/45/90 in the various quadrants, so it's not too onerous to memorize the trig functions of these.