Derivatives of Inverse Trig Functions

# Derivatives of Inverse Trig Functions - Derivatives of...

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In this section we are going to look at the derivatives of the inverse trig functions. In order to derive the derivatives of inverse trig functions we’ll need the formula from the last section relating the derivatives of inverse functions. If f(x) and g(x) are inverse functions then, Recall as well that two functions are inverses if and . We’ll go through inverse sine, inverse cosine and inverse tangent in detail here and leave the other three to you to derive if you’d like to. Inverse Sine Let’s start with inverse sine. Here is the definition of the inverse sine. So, evaluating an inverse trig function is the same as asking what angle ( i.e. y ) did we plug into the sine function to get x . The restrictions on y given above are there to make sure that we get a consistent answer out of the inverse sine. We know that there are in fact an infinite number of angles that will work and we want a consistent value when we work with inverse sine. When using the range of angles above gives all possible values of the sine function exactly once. If you’re not sure of that sketch out a unit circle and you’ll see that that range of angles (the y ’s) will cover all possible values of sine. Note as well that since

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## This note was uploaded on 11/06/2011 for the course MATH 151 taught by Professor Sc during the Fall '08 term at Rutgers.

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Derivatives of Inverse Trig Functions - Derivatives of...

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