find the exact values of the 6 trig function for a) 240 degree and b) 13π/4

Again, such questions can be greatly simplified by remembering that ...

... sin/cos are periodic by 2π (angle α=240 is equivalent to 240-360= -120 while angle β = 8π/4 + 5π/4 = 16π/4 - 3π/4 is equivalent to 5π/4 or to -3π/4) ... while ...

... tan/cot are periodic by π (angle α=240 is equivalent to 240-180= 60 while angle β = 12π/4 + π/4 is equivalent to π/4).