Context :

Aims : NGC 362 is a bright southern globular cluster in the foreground of the Small Magellanic Cloud ( SMC ) , for which no extensive variability survey has ever been done .
Finding regularly pulsating RR Lyrae stars in the cluster can lead to improved metallicity and distance estimates of the system , while other types of variable objects may be used to confirm the results .

Methods : Time-series CCD photometric observations have been obtained .
Light curves have been derived with both profile fitting photometry and image subtraction .
We developed a simple method to convert flux phase curves to magnitudes , which allows the use of empirical light curve shape vs. physical parameters calibrations .
Periods and light curve parameters of the detected variable stars have been determined with Fourier analysis , phase dispersion minimization and string-length minimization .
Using the RR Lyrae metallicity and luminosity calibrations , we have determined the relative iron abundances and absolute magnitudes of the stars .
The color-magnitude diagram has been fitted with Yale-Yonsei isochrones to determine reddening and distance independently .
For five RR Lyrae stars we obtained radial velocity measurements from optical spectra .

Results : We found 45 RR Lyr stars , of which the majority are new discoveries .
While most of them are cluster members , as shown by their radial velocities and positions in the color-magnitude diagram , we also see a few stars in the galactic field and in the outskirts of the SMC .
About half of the RR Lyraes exhibit light curve changes ( Blazhko effect ) .
The RR Lyrae-based metallicity of the cluster is [ Fe / H ] = -1.16 \pm 0.25 , the mean absolute magnitude of the RR Lyrae stars is M _ { V } = 0.82 \pm 0.04 mag implying a distance of 7.9 \pm 0.6 kpc .
The mean period of RRab stars is 0.585 \pm 0.081 days .
These properties place NGC 362 among the Oosterhoff type I globular clusters .
The isochrone fit implies a slightly larger distance of 9.2 \pm 0.5 kpc and an age of 11 \pm 1 Gyr .
We also found 11 eclipsing binaries , 14 pulsating stars of other types , including classical Cepheids in the SMC and 15 variable stars with no firm classification .

Conclusions : NGC 362 hosts a large number of RR Lyrae stars , which makes the cluster a potentially important test object for studying the Blazhko effect in a chemically homogeneous environment .