Question

Explain how you will find the coordinates of P(14π/3) if you know the coordinates of P(π/3).

Answer 1

Since your title is Trigonometry, I will assume that 14π/3 is a rotation angle

expressed in radians
one rotation is 2π, and since
14π/3 ÷ 2π = (2 1/3)π = 2π + 1/3 π

all trig ratios of 14π/3 are equal the absolute values of
the trig ratios of π/3 or 1/3 π , taking into consideration the rules of CAST

(if you want to think of degrees:
14π/3 radians = 840 *
840° = 720° + 120° , but 120° = 2*60°
π/3 is 60°, so we have to also consider the CAST rule

sin 840° = sin 120° = sin 60°, because sine is + in both I and II
cos 840 = cos 120 = -cos60°, because cosine is + in I and IV, not in II
tan 840 = tan 120 = -tan 60°, because tangent is + in I and III, not in II )