Even And Odd Trig Functions

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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:-
  1. Sin (-x) = - Sin (x), hence by definition it is odd function
  2. 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) = ½

Therefore,

Sin (-30) = - Sin (30) = - ½

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.
 

 
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