Degree of trigonometric polynomial How can i determine degree of trigonometric polynomial? I know the highest power in a univariate polynomial is known as its degree, but what is degree of trigonometric polynomial? Please help me

To determine the degree of an algebraic polynomial, we bring to to the canonical form $$c_0+c_1 x+c_2 x^2+ \dots +c_nx^n\tag{1}$$ with $c_n$ not equal to $0$. The number $n$ is  the degree of this polynomial. 
To determine the degree of an trigonometric polynomial, we also bring to to the canonical form 
$$a_0+ a_1 \cos x+b_1\sin x  +  a_2 \cos 2x+b_2 \sin 2x  + \dots + a_n\cos nx+b_n \sin nx \tag{2}$$ with at least one of $a_n,b_n$ not equal to zero.  The number $n$ is  the degree of this trigonometric polynomial. 
Alternatively, you can write (2)  in complex form, as a sum of $c_ke^{ikx}$, $c_k \in\mathbb C$. Then the degree is  the maximum of $|k|$ among the terms with $c_k\ne 0$. This is closer to (1), especially because $e^{ikx}$ is $e^{ix}$ raised to power $k$.
