Shinjin (信心) is a central concept in Japanese Pure Land Buddhism which indicates a state of mind which totally entrusts oneself to Amida Buddha's other-power (Japanese: tariki), having utterly abandoned any form of self effort (J: jiriki) or calculation (J: hakarai). The term has been variously translated as "faith", "entrusting heart", "true entrusting", "mind of true faith", and so on. It is also often left untranslated in English language publications on Shin Buddhism. It is a key concept in the thought of Shinran (1173–1263), the founder of Jōdo Shinshū. Shinran's concept of shinjin is rooted in the concept of faith found in Indian Pure Land scriptures and in the teachings of the Chinese Pure Land Buddhist masters Tanluan and Shandao, who also emphasized the importance of faith in Amitābha Buddha.
The term Shinjin (Chinese: "Xìnxīn") is also used in other Buddhist traditions occasionally, though not as commonly as in Pure Land. The influential early Chan Buddhist poem "Xìnxīn Míng (Faith-Mind Inscription)" is one example.
Indian precedents.
The original Sanskrit term that was translated into shinjin was prasanna-cittā. In Buddhist Hybrid Sanskrit and in Pali, prasanna (Pali: pasanna) can indicate belief, trust or faith (according to "Edgerton Buddhist Hybrid Sanskrit Dictionary", p. 388; and the "Pali Text Society's Pali-English Dictionary"), thus the term can mean "faithful mind". However, the term prasanna also means "clarity" and "pure" in Sanskrit, thus the term can also mean "clear mind" or "pure mind". Furthermore, the term can also mean pleased, peaceful, serene, delighted, happy. Thus, "prasanna" may have had multiple connotations.
The term "prasanna-cittā" appears in a key passage of the "Amitayus Sutra" which discusses the 18th vow of Amitabha Buddha (when he was Dharmakara bodhisattva). This passage is central to Pure Land Buddhist through, for it discusses the fundamental vow (hongan) of Amitabha. The standard Chinese edition of Saṅghavarman states:If, when I attain buddhahood, sentient beings in the lands of the ten directions who sincerely and joyfully entrust themselves [prasanna-cittā] to me, desire to be born in my land, and think of me even ten times should not be born there, may I not attain perfect enlightenment. Excluded, however, are those who commit the five grave offenses and abuse the Right Dharma.Luis O. Gomez, translating from the Sanskrit, uses "serene trust" for prasanna-cittā. 
Another syonymous term is cittaprasāda (settled faith, pure faith). According to the "Dà zhì dù lùn", cittaprasāda can be attained by sentient beings through the actions of the Buddha:All his bodily actions, all his vocal actions and all his mental actions accompany knowledge ("sarvāṇi kāyavāgmanaskarmāṇi jñānānuparivartini"). – In the Buddha, all bodily, vocal and mental actions are preceded by knowledge ("jñānapūrvaṃgama") and, subsequently, accompany knowledge ("jñānānuparivartin"). Of all the bodily, vocal or mental actions of the Buddha, there is not one that is not useful to beings: this is why it is said that his actions are preceded by knowledge and accompany knowledge. Thus it is said in a sūtra: “In the Buddhas, even the out breath ("praśvāsa") and the in breath ("āśvāsa") are useful to beings.” How, then, would their bodily, vocal and mental actions not be useful to them? The wicked who smell the perfume ("gandha") of the breath ("ānāpāna") of the Buddha obtain pure faith ("cittaprasāda") and love the Buddha.In Bodhiruci's translation of Vasubandhu's "Upadeśa on the Sūtra of Amitāyus Buddha" (無量壽經優波提舍), the term 信心 is used in the following passage:How does one contemplate? How does one produce pure faith [信心]? If a good man or woman practices the Five Gates of Mindfulness and if that person's practice is perfected, ultimately that person will obtain birth in the Land of Peace and Bliss and will see Amida Buddha. What are the Five Gates of Mindfulness? The first is the Gate of Worship. The second is the Gate of Praise. The third is the Gate of Aspiration. The fourth is the Gate of Contemplation. The fifth is the Gate of Merit Transference. Furthermore, Vasubandhu speaks of three key qualities bodhisattvas cultivate to achieve birth in the Pure Land: (1) the undefiled pure mind that does not seek anything, (2) the peaceful pure mind that seeks to eliminate suffering in all beings, (3) the blissful pure mind which seeks to bring all beings to Buddhahood. Vasubandhu also goes on to state that "the above-mentioned three types of minds, namely, the undefiled pure mind, the peaceful pure mind and the blissful pure mind are condensed into one which is the perfection of the exquisite, blissful, superior and true mind." He also states that this comprises Wisdom (Prajña), Compassion and Expediency (Upaya).
Precedents in Chinese Buddhism.
In Chinese Buddhism, the term 信心 ("Xìnxīn") and other related compounds (such as 信心門, xìn xīn mén, "gate of the faith mind") appear in various sources like the "Mahāparinirvāṇasūtra" and the "Shi Moheyan Lun" (釋摩訶衍論, a commentary to the "Awakening of Faith"). Various Chinese Mahayana sutras contain related terms for faith, such as jìng xìnxīn (淨信心, serene faith mind) which appears in the "Mahāratnakūṭasūtra" and xìnxīn qīngjìng (信心清淨, pure faith mind) which appears in various Prajñaparamita sutras like the "Diamond Sutra".
In Chinese Pure Land Buddhism, faith in the Buddha Amitābha and his power to transport all beings to the Pure Land was a central element. It was discussed by various Pure Land masters, including Tanluan and Shandao.
Tanluan.
The Chinese Pure Land patriarch Tanluan gives faith a central role for the practice of Pure Land Buddhism. According to Tanluan, reciting the names of the Buddha Amitabha has the power to eliminate ignorance and satisfy all of one's aspirations. However, some people are not in true union with the name of the Buddha and this is because of a lack of faith. If one's faith is not honest, definitive, continuous and one-pointed, then one will not be able to attain union (相應 xiāngyìn, or "association", "to be bound to", yoga) with the true meaning of the Buddha's name. 
Shandao's triple mind of faith.
The central concept of Pure Land faith taught by Shandao is the triple mind or "three minds" (三心), which is the mental attitude needed to attain birth in the Pure Land of Amitabha. The "Three Minds" are found in Shandao’s extant works, like his commentary on the "Amitayus Contemplation Sutra" ("Guan Wuliangshou Jing" 觀無量壽經) and in his "Hymns in Praise of Birth" ("Wangsheng Lizan Ji," 往生礼讃). They are also listed in the "Contemplation Sutra" and taught by other Chinese commentators like Jingying Huiyuan. According to Shandao, the "Three Minds" represent three qualities necessary for practitioners seeking birth in the Pure Land of Amitābha Buddha. They are:
Shandao emphasized the importance of these three qualities as internal states that align the practitioner with Amitābha’s vow. By cultivating these three mental attitudes, Shandao taught that one could ensure rebirth in the Pure Land regardless of one's level of doctrinal understanding or meditation skill.
Japanese Pure Land.
Shinjin (信心, often translated as "true entrusting" or "mind of true faith") is a general Japanese Buddhist term used in other traditions, especially in Japanese Pure Land Buddhism. Hōnen 法然 (1133–1212), the founder of Jōdo-shū and Shinran's teacher, discussed the idea of Shinjin basing himself on the teaching of Shandao about the threefold mind (sanshin 三心 ). However, the term Shinjin is particularly associated with the Jōdo Shinshū teaching of Shinran, in which it becomes the central and singular element of a person's liberation. 
Hōnen.
Hōnen generally follows Shandao's explanation of the threefold mind or threefold devotional heart and exhorts his followers to "cultivate the threefold devotional heart". Hōnen explains the threefold mind as follows: Put succinctly, the Three-fold Devotional Heart is nothing more than just the earnest desire for birth in the Pure Land. The wish for birth in the Pure Land, truthfully and without pretension, is called the "Genuine Heart." The purity of this heart, which bears no doubt even for a moment that the vocal Nembutsu leads to Buddha Amitabha to come to welcome one at the time of death, is called the "Profound Heart." One's desire to be born in that Pure Land and to transfer one's accumulated merits of practice and wholesome deeds for Ojo (birth in the Pure Land) are called the "Heart Aspiring Ojo through the Transference of Merit." In short, if one wishes for birth in the Pure Land with purity of heart, one will by nature embody the Three-fold Devotional Heart.Furthermore, according to Hōnen, the triple mind is "the heart of the essential vow, which Amida Buddha made when he was a bodhisattva Dharmakara". He also writes that it is not necessary to have some deep scholarly understanding to develop this faith, since:The threefold devotional heart was designed for even the most ignorant. Those who are not even aware of the name of the threefold devotional heart can also possess the three parts of it without knowing anything about them. Accordingly when one hears that Amida Buddha will certainly receive us into the Pure land through total reliance on him and the single-hearted recitation of his name - if, with deep faith in these words without questioning, one desires to be welcomed by him and recites his name - one will embody the threefold devotional heart naturally because one's heart is in accordance with the threefold devotional heart. Hōnen also taught that there are two types of the threefold heart: "the threefold devotional heart that encompasses wisdom and the threefold devotional heart that encompasses practice." The threefold heart of faith which encompasses wisdom is developed gradually through study of the Pure Land scriptures. The threefold heart of practice meanwhile is "devotion in the recitation of nembutsu, unshakable faith, and aspiration for birth in the Pure Land." 
In Shinran and Jōdo Shinshū.
Shinjin became a major element in the teachings of Shinran, who is credited with transforming and systematizing Pure Land beliefs into the school of Jōdo Shinshū (浄土真宗, "True Pure Land School"). For Shinran, Shinjin represented a radical interpretation of faith as total reliance on Amitābha (Jp: Amida) Buddha’s saving vow, contrasting with the traditional Buddhist emphasis on self-power ("jiriki" 自力) practices such as meditation and ethical perfection. Furthermore, Shinran saw shinjin as the essence of Pure Land Buddhism, as he states in "Notes on 'Essentials of Faith Alone:" "Know that the true essence of the Pure Land teaching is that when we realize true and real shinjin, we are born in the true fulfilled land".
According to the Shinran, all the various mental qualities discussed by the past masters like Vasubandhu (who speaks of the undefiled mind, the peaceful mind and the blissful mind, as well as the five mindfulnesses) and Shandao (who teaches the three minds), are really all aspects of one quality, "Shinjin". Shinran draws on passages in Vasubandhu's "Upadeśa on the Sūtra of Amitāyus" where he speaks of the "single mind" or "single mindedness" to support this position. 
In Shinran's Jōdo Shinshū tradition of Pure Land, "shinjin" denotes an absolute and singular entrustment in Amitābha’s Primal Vow (Jp: hongan), which promises salvation to all beings who sincerely call upon his name (Nembutsu). Shinjin refers to a unified state of faith, trust, and humility. However, Shinjin is not just trust, it is a multifaceted phenomenon which Shinran describes as follows:We see clearly that sincere mind is the mind that is the seed of truth, reality, and sincerity; hence, it is completely untainted by the hindrance of doubt. Entrusting is the mind full of truth, reality, and sincerity; the mind of ultimacy, accomplishment, reliance, and reverence; the mind of discernment, distinctness, clarity, and faithfulness; the mind of aspiration, wish, desire, and exultation; the mind of delight, joy, gladness, and happiness; hence, it is completely untainted by the hindrance of doubt. Aspiration for birth is the mind of wish, desire, awakening, and awareness; the mind of accomplishment, fulfillment, performance, and establishment. It is the mind of great compassion directing itself to beings; hence, it is completely untainted by the hindrance of doubt.  Here, in considering the literal meanings of the terms for them, we find that the three minds are the mind of truth and reality, free of any taint of falsity; they are the mind right and straightforward, free of any taint of wrong and deceit. Truly we know, then, that this is called shinjin* because it is untainted by the hindrance of doubt. Shinjin* is the mind that is single. The mind that is single is shinjin that is true and