What do we mean by even trigonometric functions Which of the

What do we mean by even trigonometric functions?

Which of the six functions fall into this category?

What do we mean by odd trigonometric functions?

Which of the six trigonometric functions fall into this category?

Give an example for your classmates to work. Ask them to use even and odd properties of trigonometric functions to find the exact value of the expression.

Solution

let f(x) be trigonometric function

even trignometric functions are the ones for which f(-x)=f(x) ,i.e, change of sign of x doesnot alter the value of function

cosine and secant functions are evenfunctions

cos(-x)=cos(x) ,sec(-x)=sec(x)

odd trignometric functions are the ones for which f(-x)=-f(x) ,i.e, change of sign of x alter the value of function

sine ,tangant ,cotsngent ,cosecant functions are evenfunctions

sin(-x)=-sin(x) , tan(-x)=-tan(x),cot(-x)=-cot(x) ,csc(-x)=-csc(x)

examples of even trigonometric functions are

cos(3x),sec(10x)

examples of odd trigonometric functions are

sin(mx),tan(5x),cot(4x),csc(10x)