The temperature dependence of magnetic anisotropy in (113)A (Ga,Mn)As layers grown by molecular-beam epitaxy is studied by means of superconducting quantum interference device magnetometry as well as by ferromagnetic resonance (FMR) and magnetooptical effects. Experimental results are described considering cubic and two kinds of uniaxial magnetic anisotropy. The magnitude of cubic and uniaxial anisotropy constants is found to be proportional to the fourth and second power of saturation magnetization, respectively. Similarly to the case of (001) samples, the spin reorientation transition from uniaxial anisotropy with the easy axis along the [(1) over bar 10] direction at high temperatures to the biaxial < 100 > anisotropy at low temperatures is observed around 25 K. The determined values of the anisotropy constants have been confirmed by FMR studies. As evidenced by investigations of the polar magnetooptical Kerr effect, the particular combination of magnetic anisotropies allows the out-of-plane component of magnetization to be reversed by an in-plane magnetic field. Theoretical calculations within the p-d Zener model explain the magnitude of the out-of-plane uniaxial anisotropy constant caused by epitaxial strain but do not explain satisfactorily the cubic anisotropy constant. At the same time the findings point to the presence of an additional uniaxial anisotropy of unknown origin. Similarly to the case of (001) films, this additional anisotropy can be explained by assuming the existence of a shear strain. However, in contrast to the (001) samples, this additional strain has an out of the (001) plane character.