TUTORIAL (1)  Domain, Range, Zeros and Vertical Asymptotes of the 6 Basic Trigonometric Functions  Answers

f(x) = sinx(x)
 domain : (∞ , +∞)
 range : [1 , 1]
 period : 2π
 zeros at x = kπ, k is an integer (k = 0 , ~+mn~ 1 , ~+mn~ 2 , ...).

f(x) = cos(x)
 domain : (∞ , +∞)
 range : [1 , 1]
 period : 2π
 zeros at x = π/2+ kπ, k is an integer (k = 0 , ~+mn~ 1 , ~+mn~ 2 , ...).

f(x) = tan(x)
 domain : all real numbers except π/2 + kπ where k is an integer.
 range : (∞ , +∞)
 period : π
 zeros at x = kπ, k is an integer (k = 0 , ~+mn~ 1 , ~+mn~ 2 , ...). (Note: tan(x) and sin(x) have the same zeros because tan(x) = sin(x) / cos(x))
 vertical asymptotes at x = π/2 + kπ, k is an integer.

f(x) = cot(x)
 domain : all real numbers except kπ where k is an integer.
 range : (∞ , +∞)
 period : π
 zeros at x = π/2+ kπ, k is an integer (k = 0 , ~+mn~ 1 , ~+mn~ 2 , ...). (Note: cot(x) and cos(x) have the same zeros because cot(x) = cos(x) / sin(x))
 vertical asymptotes at x = kπ, k is an integer.

f(x) = sec(x)
 domain : all real numbers except π/2 + kπ where k is an integer.
 range : (∞ , 1] U [1 , +∞)
 period : 2π
 sec(x) has no zeros.
 vertical asymptotes at x = π/2 + kπ, k is an integer.

f(x) = csc(x)
 domain : all real numbers except kπ where k is an integer.
 range : (∞ , 1] U [1 , +∞)
 period : 2π
 csc(x) has no zeros.
 vertical asymptotes at x = kπ, k is an integer.
TUTORIAL (2)  Relationship Between Basic Trigonometric Functions
 sin(x) = cos(x&pi/2) , cos(x) = sin(x+&pi/2)
 Since csc(x) = 1 / sin(x), the values that make sin(x) = 0 will create a division by zeros of the form 1/0 for csc(x) meaning that there is a vertical asymptotes at the same x values.
 Since sec(x) = 1 / cos(x), the values that make cos(x) = 0 will create a division by zeros of the form 1/0 for sec(x) meaning that there is a vertical asymptotes at the same x values.
 sin(x) = cos(xπ/2) , sec(x) = 1/cos(x) , csc(x) = 1/cos(xπ/2) , tan(x) = cos(xπ/2) / cos(x) ,
cot(x) = cos(x) / cos(xπ/2)
 cos(x) = sin(x+π/2) , sec(x) = 1/sin(x+π/2) , csc(x) = 1/sin(x) , tan(x) = sin(x) / sin(x+π/2) ,
cot(x) = sin(x+π/2) / sin(x)
More references and links related to trigonometric functions and their properties.
