The Goal

Find

The Mistake

Find the mistake:

(Roll the mouse over the math to see a hint in red)

The Correction

(Roll the mouse over the area above to see the correction in blue)

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.