Common Trigonometry Mistakes
Example: Value of inverse cosine

The Goal



The Mistake

Find the mistake:


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The Correction


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An Explanation

In this mistake the notation cos-1(x) has been misunderstood to mean 1/cos(x). That interpretation might seem to be a natural extension of notation such as cos2(x), which does mean (cos(x))2, and cos-2(x), which does mean 1/(cos(x))2. However, for any function f(x), by convention when we write f-1(x), we mean instead the inverse function for f(x). So cos-1(x) means the inverse cosine of x, that is, the function that undoes the cosine function.

Visit Trigonometry Facts for help in learning values of the inverse trigonometric functions.

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