Question

Which of the following fuctions are odd or even or neither?
a) F(x)=cot x +4cosec x +x
b) F(x)= sec x +4cos x +3x^2
c) F(x)=sin x +cos x

Answer 1

Answer:

In this lesson we will look at how to determine whether a Trigonometric Function is Even, Odd or Neither.

What is an even function?

1. An even function is symmetric about the y-axis.

2. f(-x) = f(x)

What is an odd function?

1. An odd function is symmetric about the origin.

2. f(-x) = -f(x)

The following table shows the Even Trigonometric Functions and Odd Trigonometric Functions. Scroll down the page for more examples and step by step solutions.

Trigonometric Even Odd Functions

Even Trigonometric Functions and Identities

Cosine function is even. cos(-x) = cos x

Secant function is even. sec(-x) = sec x

Odd Trigonometric Functions and Identities

Sine function is odd. sin(-x) = - sin x

Cosecant function is odd. csc(-x) = - csc x

Tangent function is odd. tan(-x) = - tan x

Cotangent function is odd. cot(-x) = - cot x

Determine whether a trigonometric function is odd, even, or neither

Examples with Trigonometric Functions: Even, Odd or Neither

Cosine function, Secant function, Sine function, Cosecant function, Tangent function, and Cotangent function

Answer 2

Answer:

Step-by-step explanation:-

Well,as you know that,

sin( -x ) = - sin x  =>f(-X)=-f(x) =>odd function

csc ( -x ) = - csc x  ;similarly odd function

cos ( -x ) = cos x ; but this is an even function; f(-x)=f(x)

sec (-x ) = sec x ; even function

tan ( -x ) = - tan x ; odd function

tan ( -x ) = - cot x ;and odd function

So now lets move to the first question

1)f(x)=cotx+4cosecx+x

ANSWER:-  odd function,

f(-x)=-cotx-4cosecx-x => -(cotx+4cosecx+x)=> f(-x)=-f(x) ,so its an odd function.

2)similarly second you solve you will get even function.

f(x)=secx+4cosx+3x*2

for f(-x) you will get same function f(-x)=secx+4cosx+3x*2, so its an even funcion.

3)Now when you come to third you will get this is nor a odd niether even function. WHY? lets check

f(x)=sinx+cosx =>f(-x)= -sinx+cosx  which is neither as equal to -f(x) nor as f(x)

so you can call it neither odd nor even

                                HOPE IT HELPED:)

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