In Naruto, the taijitu (Yin Yang symbol) can be seen surrounded by the Bagua (Eight Trigrams) in the divination field of the Hyuga Clan, whose fighting style may have been based on Baguazhang (Eight Trigram Palm), one of the three Chinese 'internal' martial arts.
On the other hand, the Uchiha Clan’s Sharingan is symbolized by the three tomoe. The mitsu-domoe may also hold a similar meaning to Yin Yang where the three tomoe separately represent earth (Yin), heaven (Yang) and the union of earth and heaven (third tomoe).

Yin, among others, is symbolized by:
Female, deficient, passive, dark – characteristics fitting Hinata
Season: Winter
Primary Element: Water
Hinata
Birth month: December
Season: Winter
Element: -
Yang, among others, is symbolized by:
Male, excessive, active, bright – characteristics fitting Sasuke
Season: Summer
Primary Element: Fire
Sasuke
Birth month: July
Season: Summer
Elements: Fire , Lightning
The Major Numbers of Yin and Yang
8 is the major number of Yin
Hinata's team number: 8
Hyuga Clan:
The Hyuga clan and it's members are well known for the use of eight divination signs, hakke (八卦), where hak is synonymous to hachi (八), meaning eight.
7 is the major number of Yang
Sasuke's team number: 7
Uchiha Clan:
The best kept secret of the Uchiha is the ability of the Mangekyou Sharingan to control the nine-tailed demon. This information was hidden in the Uchiha clan's secret meeting place, located at the Nakano shrine under the seventh tatami mat.
The Minor Numbers of Yin and Yang
6 is the minor number of Yin and 9 is the minor number of Yang
Hinata's birth date: December 27 (12 27);
Sasuke's birth date: July 23 (07 23).
Adding these numbers, like two halves of a whole, the sum would be 69. Moreover, by mere appearance, the number 69 closely resembles the Yin Yang symbol.
Yin and Yang are Complementary Opposites I
The similarities of Hinata and Sasuke
Noble birth: Hyuga
Bloodline Limit: Byakugan (eye technique)
Sought the acknowledgement of a parent
Noble birth: Uchiha
Bloodline Limit: Sharingan (eye technique)
Sought the acknowledgment of a parent
Relationship with the "Older Brother"
In his younger days, Hizashi asked Neji to protect Hinata and
the Hyuga.
[imghttp://julywintertheories.weebly.com/uploads/7/0/8/9/7089618/9215948.jpg?244][/img]
Before his death, Fugaku asked Itachi to take care of Sasuke.

Rivalries despite the promises.


Teamwork with Sibling in the 4th shinobi war.
Neji and Hinata against White Zetsu

Sasuke and Itachi gainst Kabuto

A White Zetsu clone captured Neji

In a subsequent but separate event, Hinata protected Neji from a White Zetsu clone (see second panel).

Kabuto's technique temporarily incapacitated Itachi

Subsequent to Itachi's temporary incapacitation, Sasuke protected Itachi with Amaterasu, stopping Kabuto from a distance.

Neji died protecting Hinata (and Naruto) from Jūbi's attacks.

Itachi died protecting Sasuke from Orochimaru
(essentially freeing Sasuke from the Cursed Seal).

Relationship with Naruto Uzumaki
Hinata protected Naruto from Pain

Sasuke protected Naruto from Haku

When Hinata appeared to have died,
Naruto fully transformed into the eight-tailed demon fox
(image shows the six-tailed transformation).

When Sasuke appeared to have died,
Naruto awakened the nine-tailed demon fox in him

Teamwork with Naruto in the 4th Shinobi War
Jūbi used Wood Style: Cutting Sprigs on the Shinobi Alliance.

Princess Kaguya unleashed an attack on Team 7.

Hinata and Sasuke (Susanoo) raised their hands to protect Naruto when others were unable.


Regrettably, some efforts are never enough.
Important Note: The following should be viewed only as Neji's metaphor, the caged bird.
Neji took the attack aimed at Hinata and Naruto.


Sasuke's Susanoo and his Hawk summoning took the attack.
Susanoo wasn't as effective while the Hawk's vital points were hit.


Neji's death caused Naruto to falter.


Previously, Shikamaru's near-death state caused Naruto to falter.


Obito attempted to give him doubts, however,
Hinata woke him from his stupor.

Sasuke woke him from his stupor.

Naruto thereafter reflected upon everyone's sacrifices. Having decided not to let them go in vain, he moved forward.


Yin and Yang are Complementary Opposites II
The opposition of Hinata and Sasuke
Hinata (Hyuga successor) is 5 years older than Hanabi.
Hinata performed Jūho Sōshiken,
Gentle Fist - Yin

Sasuke is 5 years younger than Itachi (Uchiha successor?).
Sasuke developed Shishi Rendan based on Rock Lee's Front Lotus, Strong Fist - Yang

Kabuto Yakushi healed Hinata during the chūnin exams.

Kabuto Yakushi tried to kill Sasuke during the chūnin exams.

The Village Hidden in the Clouds once attempted to kidnap Hinata,
in hopes of unlocking the secrets of the Byakugan.

Sasuke tried but failed to capture Killer Bee (the 8-Tails jinchūriki)
of the Village Hidden in the Clouds for Akatsuki.

Hinata tried to protect Naruto from Pain,
and confessed how she felt about him.

Sasuke tried to protect Naruto from Haku,
and confessed how he felt about him.

Right is Yin and Left is Yang

With reference to Zetsu,
Yin - Black (right) ; Yang - White (left)
With reference to Hinata's JuuHo: Soushiken

Yin - komainu, right hand ; Yang - shishi, left hand
Note how the boxed lion seemed to have a relatively closed jaw compared to the other.
JuuHo: Soushiken may possibly be inspired by komainu (literally, Korean lions), a pair of lions usually found at the entryway of shrines. They are believed to ward off evil, and are almost identical in appearance except one lion has it's mouth closed (komainu, Yin counterpart), the other open (shishi, Yang counterpart). During the Heian period, they were identified separately but eventually, both became known as komainu.
With reference to Sasuke's Sharingan (appearance of second tomoe)

Yin - even number, right eye ; Yang - odd number, left eye
Presumption 01: When one eye technique is not in combination with another (this includes Madara's Rinnegan which both progressed from Sharingan shortly before his death), the polarity (Yin/Yang) takes into consideration the family of origin of the eye technique. These are:
Yin - Hyuga, emphasis of right Byakugan
Hinata and the Right Eye in Ch 437

Ao and his Byakugan
Yang - Uchiha, emphasis of left Sharingan
Sasuke and the Left Eye in Ch 218, 397 and 673, respectively.



Kakashi and his Sharingan

Shisui and Koto Amatsukami

Madara and his Sharingan
(*following the transplant of his Rinnegan to Nagato)

Presumption 02: Although irrelevant, in an interview wherein Mr. Kishimoto was asked, "If a Hyuga and an Uchiha had a child together, what eyes would s/he get?" Mr. Kishimoto answered, "His right eye would be a Sharingan. Meaning that the left one would be a Byakugan!"
In the combination of the Byakugan and the Sharingan, the polarity of the eyes themselves may be taken into consideration. That is:

Yin - Sharingan on the right eye
Yang - Byakugan on the left eye
In Chapter 671: Naruto and the Sage of Six Paths...!!, Naruto and Sasuke were the receiving ends of the powers of Hagoromo Ōtsutsuki. Asked to lift their dominant arms, Naruto raised Right (Yin) while Sasuke raised Left (Yang).


Emphases of the dominant arms may be similarly seen whether Naruto and Sasuke are fighting each other or together against someone else.


There was no depiction of dominant arms with regards to Hinata and Neji. However, briefly shown in the combined technique, Hakke Kūhekishō,

Hinata raised her Right hand (Yin) while Neji raised his Left hand (Yang).
There is a Yang in Yin and a Yin in Yang
There are no absolutes in Yin and Yang
The Hyuga Clan

Yin: Gentle Fist
inner Yang: Byakugan
Within the Hyuga Clan
Chapter 79: The Hyuga Clan

Yin: Cadet Branch, inner Yang: Neji
Yang: Main Branch, inner Yin: Hinata
Yin: Hinata
inner Yang: "Sunny Place"
Yang: Neji
inner Yin: Darkness
(Naruto saved him)
Yin Hinata: Jūho Sōshiken

Jūho Sōshiken is a Gentle Fist (Yin) technique.
Yang Neji: Hakkeshō Kaiten

While also a Gentle Fist (Yin) technique,
Kaiten literally means rotating heaven; Heaven is a symbol of Yang.
The Uchiha Clan

Yang: Fire
inner Yin: Sharingan
Within the Uchiha Clan
Chapter 384: Two Paths...

Yin: Itachi
Yang: Sasuke
Yin: Itachi
inner Yang: Will of Fire
Yang: Sasuke
inner Yin: Darkness
Yin Itachi: Water

Based on the Five Elements, Water is Yin.
Yang Sasuke: Lightning

Based on the Five Elements,
Lightning (synonymous to Heaven) is Yang.
As Hyuga, Hinata and Neji may be predominantly Yin but Neji's ability to perform Kaiten may also make him inclined to Yang.
As Uchiha, Itachi and Sasuke may be predominantly Yang but Itachi's affinity with Water may also make him inclined to Yin.
On a similar but separate note, when Naruto and Sasuke received the Yang and Yin powers from Hagoromo, respectively, it may appear that:
The power of Yang within Yin (Naruto).

The power of Yin within Yang (Sasuke).

Yin is passive where Yang is active
Yin Hinata: Hakke Rokujūyon Shō
Yang Neji: Hakke Rokujūyon Shō
Yin Itachi: Amaterasu and Tsukuyomi

Yang Sasuke:
Enton: Kagutsuchi and break-through of Tsukuyomi

Based on developments, the Yin counterparts may seem passive while Yang counterparts may seem active (i.e. surpassing).
Notes
Other characters seen to symbolize Yin and Yang
Sasuke and Naruto

Yang: Fire, Lightning
inner Yin: Sharingan
Yin: Wind
inner Yang: Life Force
more in: Naruto x Sasuke: Bonds
Gaara and Rock Lee

Yin: Wind
Yang: Strong Fist
Madara and Hashirama

Yang: Fire
inner Yin: Sharingan
Yin: Water
inner Yang: Wood *kekkei genkai
more in: Rikudō Sennin, Uchiha and Senju
Danzō and Hiruzen

Yin:
"Foundation hidden in
the darkness"
Yang:
"Leaf upon which light shone"
4th Character Official Databook
online leak: first week of November 2014
In theory,
Hinata

Yin: Gentle Fist
inner Yang: Byakugan
Sasuke

Yang: Fire, Lightning
inner Yin: Sharingan
Based on the 4th Character Official Databook,
Hinata and Sasuke have gained chakra nature types with polarities which may theoretically compensate for what they lacked previously:

Yang: Fire, Lightning

Yin: Water, Wind
*Sasuke has also gained Earth (Yin Yang),
Yin Style and Yang Style.
From being predominantly Yin (Hinata) or predominantly Yang (Sasuke) to a full Yin-and-Yang.

Yin: Gentle Fist
inner Yang: Byakugan
Yang: Fire, Lightning

Yang: Fire, Lightning
Yin: Yin Style
Yin: Wind, Water
inner Yang: Yang Style
Yin Yang: Earth






