# Help with $\cos^{\frac 32}(x)$

I'm looking at putting the following in an excel formula but need help. $\cos^{\frac 32}(x)$

So how do you calculate $\cos$ to the power of $(3/2)$?

Thanks!

• Not sure I understand. $\cos^{3/2}x$ means $(\cos x)^{3/2}$. – almagest May 21 '16 at 8:57
• Excel has no difficulty with things like =3^(3/2) – almagest May 21 '16 at 9:04

The notional format should he =(cos(x))^(3/2), where x is either a cell reference or a number etc.. But:
The problem is that Excel (and Gnumeric and I expect other) uses logs to compute arbitrary powers, so if $\cos(x)< 0$ it will fail. Which is not an error as the default data type is float (or rather double ) and the result is undefined for that data type. But this will also fail at time when you might expect it to work.
As as example of it failing when it could in principle return a float is (-1)^(1/3)
Not quite sure what your question is, but obviously $\cos^{\frac{3}{2}}(x)=(\cos(x))^{\frac{3}{2}}$ or alternatively $\cos^{\frac{3}{2}}(x)= \sqrt{\cos^3(x)}$ .