Also, the output of a linear system can contain harmonics (and have a smaller fundamental frequency than the input) even when the input is a sinusoid. For example, consider a system described by y ( t ) = ( 1.5 + cos ⁡ ⁡ ( t ) ) x ( t ) . It is linear because it satisfies the superposition principle. However, when the input is a sinusoid of the form x ( t ) = cos ⁡ ⁡ ( 3 t ) , using product-to-sum trigonometric identities it can be easily shown that the output is y ( t ) = 1.5 cos ⁡ ⁡ ( 3 t ) + 0.5 cos ⁡ ⁡ ( 2 t ) + 0.5 cos ⁡ ⁡ ( 4 t ) , that is, the output doesn't consist only of sinusoids of same frequency as the input (3 rad/s), but instead also of sinusoids of frequencies 2 rad/s and 4 rad/s ; furthermore, taking the least common multiple of the fundamental period of the sinusoids of the output, it can be shown the fundamental angular frequency of the output is 1 rad/s, which is different than that of the input.