yes
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Precalculus is supposed to be a stringent and comprehensive review of both algebra and trigonometry. This is in preparation for calculus which uses both algebra and trig extensively.
It's a high school/college class wherein you learn about functions, trigonometry, advanced algebra, and many other things in preparation. See Wikipedia for more info.
I think is better to take precalculus first, then take calculus. When you take calculus, it is better to take it in three different semesters, first caculus1, then calculus2 and 3. If you go step by step, I think is better to appropriate the knowledge. If you have enough time to study, then do not hurry up. However, if you believe in yourself that you can do it, based on your previous knowledge, then do it.
yes. as the name implies, pre-calculus is essential in Calculus. Much of the trigonometry and the ideas will carry into the carious Calculus classes.
No calculus is harder, because calculus is basically a combination of algebra and trigonometry, so you need algebra to do calculus. Also, calculus involves limits, differentiation, and integration. Integration makes algebra look like kindergarten. +++ Meaningless question, ditto with the answers I'm afraid. These are not separate entities but all fields of mathematics, and you use algebra in expressing and solving mathematical problems. Calculus is NOT "basically a combination of algebra and trigonometry". You can differentiate and integrate trig. functions, but although calculus alone does not rely on trigonometry for its existence, its manoeuvres are all algebraic steps. As to comparative difficulty, that is entirely down to you. If you find algebra difficult you will find trigonometry and calculus difficult, because algebra is used to describe those two (and any other) mathematical process. Algebra is not an isolated topic!