Some instructors recommend pivoting 90 degrees when executing a roundhouse kick, cocking the knee of their kicking leg, then extending it into the kick, with the knee at a right angle to the target. Others pivot 180 degrees to deliver the roundhouse kick, with their knee pointed forward toward the target, which means the kicker must view the target over the shoulder, which is an awkward twist. However, the 180 degree pivot generates maximum power. Others pivot 160 degrees, which allows the knee to be brought up and still generate plenty of power and permits the kicker to view the target better.
For a hook kick, the pivot is 180 degrees so the kicking leg can extend straight toward the side of the target and still achieve the whip-like hooking motion.
For side kicks, some instructors advocate 90-degree pivots, making the technique a quick knee cock, followed immediately by the side kick. Traditional Taekwondo uses a 180 degree pivot that makes the kicks appearing a little like a back kick, which means the kicker must view the target over the shoulder.
Sliding side kicks require a 180 degree pivot. Modern Contemporary Taekwondo uses 160 degree pivot so you can see the target easier. Again the 180 degree pivot generates the most powerful kick.
Spinning hook and back kicks require a 180-degree pivot. Anything less will place unnatural torque on the stationary knee.
Knowledge of different kick pivots is important for a number of reasons. An improper pivot decreases power, disrupts balance, obstructs your view of your target and may damage the joints of your stationary leg.