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Are trigonometric equations and trigonometric identities are the same thing?
In a trigonometric equation, you can work to find a solution set which satisfy the given equation, so that you can move terms from one side to another in order to achieve it (or as we say we operate the same things to both sides). But in a trigonometric identity, you only can manipulate separately each side, until you can get or not the same thing to both sides, that is to conclude if the given identity is true or false.
What is the term trigonometry identity?
Trigonometric identities are trigonometric equations that are always true.
How would you explain to someone who has not yet studied trigonometry the difference between an identity and an equation?
An identity is true for all values of the variable whereas an equation is true for only a finite number of values.For example,Identity: (x + 2)3 = x3 + 6x2 + 12x + 27 is true, whatever the value of x.ButEquation: x3 - x = 0 is true only when x = -1, 0 or 1.
How do you verify a trig identity?
Transform one side into the other, or both sides into a third thing.
Definition of complement of a set?
S', the complement of a set S, in the context of the universal set U, is the set of all elements of U that are not in S. It is important to note that a complement is defined only in terms of the universal set. The following, rather crude example illustrates the point. Suppose S is the set of all boys. Then S' may be the set of all girls if U = youngsters; or S' = set of all girls, women and men if U = people; or S' = set of all girls, women, men, dogs, cats, cows, ... if U = mammals; and so on. As you see, changing U alters S'.
