Even and Odd Trig Functions - Trigonometry Online Tutoring

Even and Odd Trig Functions - Trigonometry Online Tutoring To understand about even and odd trig functions, it is first important to understand the concept of even and odd trig functions. A function is said to even function if the following relation persists:- The relation for even function is f (-x) = f(x) And a function is said to be odd function if the following relation persists:- The relation for odd function is f (-x) = - f (x) In case of even and odd trig functions, the following are the main even as well as odd functions:- Sin (-x) = - Sin (x), hence by definition it is odd function Cos (-x) = Cos (x), hence by definition it is even function It is important to note that tan (x) and cot (x) are both odd functions. Question 1:- Evaluate the value of Sin (-30) and tell whether it is even or odd function. Solution 1:- Here in this question we need to evaluate the value of Sin (-45) We know that Sin (-30) = - Sin (30) And we know that the value of Sin (30) = Therefore, Sin (-30) = - Sin (30) = - Since in this case the relation f(-x) = - f(x) , therefore Sin (-30) is odd function. Question 2:- Evaluate the value of tan (-45) and tell whether it is even or odd function. Solution 2:- Here in this question we need to evaluate the value of Sin (-45) We know that tan (-45) = - tan (45) And we know that the value of tan (45) = 1 Therefore, tan (-45) = - tan (45)= -1 Since in this case the relation f(-x) = - f(x) , therefore tan (-45) is odd function.