calculus - Evaluating $lim_{xto 0^+} (sin x)^x$

Evaluate the following limit.

$$\lim_{x\to 0^+} (sin\ x)^x$$

What i have tried:

$$ln\ [\lim_{x\to 0^+} (sin\ x)^x]$$

$$\lim_{x\to 0^+} ln\ (sin\ x)^x$$

$$\lim_{x\to 0^+} \frac{ln\ (sin\ x)}{\frac{1}{x}}$$

Applying l'hopital's rule.

$$\lim_{x\to 0^+} \frac{cot\ x}{-x^{-2}}$$

If i keep applying l'hopital's rule, i get indeterminate form. Is what Iam doing right ?