Testing for Symmetry...3

[nycmathguy]

How do you test trigonometric functions for Symmetry?

Do you have two examples to show me?

Thanks

 

[MathLover1]

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




.

 

[nycmathguy]

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