Testing for Symmetry...3

Joined
Jun 27, 2021
Messages
5,386
Reaction score
422
How do you test trigonometric functions for Symmetry?

Do you have two examples to show me?

Thanks
 
The cosine is known as an even function, and the sine is known as an odd function. Generally speaking,

f(x) is an even function if f(-x) =f(x)

and odd if f(-x) = -f(x)

The cosine and sine functions satisfy the following properties of symmetry:

cos(-θ) = cos(θ) => symmetry about y-axis
sin(-θ) = -sin(θ) => symmetry about origin

also

tan(−θ)=−tan(θ)=> symmetry about origin

cot(−θ)=−cot(θ)=> symmetry about origin

csc(−θ)=−csc(θ)=> symmetry about y-axis

sec(−θ)=sec(θ)=> symmetry about y-axis




.
 
The cosine is known as an even function, and the sine is known as an odd function. Generally speaking,

f(x) is an even function if f(-x) =f(x)

and odd if f(-x) = -f(x)

The cosine and sine functions satisfy the following properties of symmetry:

cos(-θ) = cos(θ) => symmetry about y-axis
sin(-θ) = -sin(θ) => symmetry about origin

also

tan(−θ)=−tan(θ)=> symmetry about origin

cot(−θ)=−cot(θ)=> symmetry about origin

csc(−θ)=−csc(θ)=> symmetry about y-axis

sec(−θ)=sec(θ)=> symmetry about y-axis




.

Test the following for symmetry.

1. csc x + sec x - 4 = 0

2. tan x/(2x) - sin (2x) = 100
 

Members online

No members online now.

Trending content

Forum statistics

Threads
2,527
Messages
9,856
Members
696
Latest member
fairdistribution
Back
Top