Question

Cot (13π/3)

Answer 1

cot (13Pi/3) = cot (3Pi + 4Pi/3) = cos (3Pi + 4Pi/3)/sin (3Pi + 4Pi/3)
Use trig identity: sin (a +b) = sin a cos b + sin b*cos a
cos (a + b) = cos a*cos b - sin a*sin b
Since sin (3Pi) = 0, cos (3Pi) = 1, we have
cos (3Pi + 4Pi/3) = cos (4Pi/3)
sin (3Pi + 4Pi/3) = sin (4Pi/3)
Finally y = cot (13Pi/3) = cos (4Pi/3)/sin (4Pi/3) = cot (4Pi/3) = cot (Pi/3) =
y = V3/3.