1. f(x) = sinx(x)
   • domain : (-∞ , +∞)
   • range : [-1 , 1]
   • period : 2π
   • zeros at x = kπ, k is an integer (k = 0 , ~+mn~ 1 , ~+mn~ 2 , ...).
   
   
   
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 , ...).
   
   
   
3. 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.
   
   
   
4. 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.
   
   
   
5. 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.
   
   
   
6. 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

1. sin(x) = cos(x-&pi/2) , cos(x) = sin(x+&pi/2)
   
   
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.
   
   
3. 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.
   
   
4. sin(x) = cos(x-π/2) , sec(x) = 1/cos(x) , csc(x) = 1/cos(x-π/2) , tan(x) = cos(x-π/2) / cos(x) ,
   cot(x) = cos(x) / cos(x-π/2)
   
   
5. 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.

• Graph Sine Function
  
  
• Sine Function
  
  
• Cosine Function
  
  
• Tangent Function
  
  
• Secant Function
  
  
• Unit Circle in Trigonometry and sin(x), cos(x) and tan(x)
  
  
• Solve Trigonometric Equations
  
  
• Graphs of Trigonometric Functions - Self Test