I'm sure this will vary by individual, but for me: 70+21 (40 * 25) * 3 + 43 + 3 * 75 + 3 (123 * 40) + 123 * 2 paper and/or calculator for the last sin(PI/3

I'm sure this will vary by individual, but for me: 70+21 (40 * 25) * 3 + 43 + 3 * 75 + 3 (123 * 40) + 123 * 2 paper and/or calculator for the last sin(PI/3) is an interesting case. I don't deal with trigonometry very often. If the problem is in the context of a project where I will be using trigonometry frequently, I'll go refresh my memory about the easier-to-retain points in addition to what already I remember: sin(N * PI) = 0, sin((2N-1/2) = -1 and sin((2N+1/2) * PI) = 1 for integer N; given a unit circle and an angle between the line segment [(0,0), (0,1)] and another line segment reaching the circumference of that circle, sin(angle) = y, cos(angle) = x of that point (x,y) on the circle (this latter used as a mental-vision sanity check on any answer proposed). If it's truly a one-off, I'll just use the calculator.