![]() ![]() ![]() The hyperbolic functions are usually defined in terms of the exponential function. ![]() It is important to know the inverse trig functions as they come in handy in many situations, like trig substitution in integral calculus. Or, using the term arcsin and not sin^-1 (though sin^-1 is more common) Like the square/square root example, if you have y=sin(x), which is y in terms of x, but you want to take that expression and find x in terms of y, then given: It is the same deal with sin and arcsin, which is conventionally written as sin^-1 x.Īrcsin is the inverse of sin, such that arcsin(sin(x)) = x, or sin(arcsin(x))=x. Now if you want to find out what x is in terms of y, then solve for x to get x=√y.Īs you know, the square operator and the square root operator are inverses of each other, that is, one "undoes" the other: √(x²) = (√x)² = x (assuming we are only interested in the principal square root). ![]()
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