please try to explain the domain & rangetable of different trigonometric function

1. f(x) = sinx(x)

• domain : (-infinity , +infinity)
• range : [-1 , 1]
• period : 2Pi

 

f(x) = cos(x)

• domain : (-infinity , +infinity)
• range : [-1 , 1]
• period : 2Pi

 

f(x) = tan(x)

• domain : all real numbers except Pi/2 + k*Pi where k is an integer.
• range : (-infinity , +infinity)
• period : Pi
• vertical asymptotes at x = Pi/2 + k*Pi, k is an integer.

 

f(x) = cot(x)

• domain : all real numbers except k*Pi where k is an integer.
• range : (-infinity , +infinity)
• period : Pi
• vertical asymptotes at x = k*Pi, k is an integer.

 

f(x) = sec(x)

• domain : all real numbers except Pi/2 + k*Pi where k is an integer.
• range : (-infinity , -1] U [1 , +infinity)
• period : 2Pi
• vertical asymptotes at x = Pi/2 + k*Pi, k is an integer.

 

f(x) = csc(x)

• domain : all real numbers except k*Pi where k is an integer.
• range : (-infinity , -1] U [1 , +infinity)
• period : 2Pi
• vertical asymptotes at x = k*Pi, k is an integer.