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Trigonometric Power Notation

It can be a source of confusion when writing down trigonometric functions when they have been raised to a power. The following convention is therefore commonly used:

\sin \theta . \sin \theta \equiv (\sin \theta)^2 \equiv \sin^2 \theta
\frac {1}{\sin \theta} \equiv \sin^{-1} \theta

A couple of things to note:

1) The dot between the two sinθ terms is just used to make it clear that they are multiplied together. (This is not the same as the dot product which can only be done between two vectors.)
2) The ≡ symbol means “identical to”, rather than just “equal to”. It’s a subtle distinction, so don’t worry if that doesn’t mean anything to you.

Note that although the inverse of a function F(x) is commonly written as F-1(x), it could get very confusing if we apply this to trigonometric functions. So:

\arcsin \theta \neq \sin^{-1} \theta

I.e. the inverse sin function (arcsin) will not be written using the negative power notation. Sometimes you may come across literature where this won’t be the case, so just be aware of this.

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