Fourier Series of a periodic function

Question 1

Zeros of Even Symmetry

Answer 1

bn = 0 (sine Terms)

Question 2

Zeros of Odd Symmetry

Answer 2

an = 0 (Cosine terms)
a0 = 0 (Average value)

Question 3

Zeros of half wave symmetry

Answer 3

n = odd harmonics only
a0 = 0 (Average value)

Question 4

Zeros of even quarter wave symmetry

Answer 4

bn = 0 (sine terms)
a0 = 0
n = odd harmonics only

Question 5

Zeros of odd quarter wave symmetry

Answer 5

a0 = 0
an = 0 (cosine terms)
n = odd harmonics only