Testing for Symmetry...3

Discussion in 'Algebra' started by nycmathguy, Jun 8, 2022.

  1. nycmathguy

    nycmathguy

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    How do you test trigonometric functions for Symmetry?

    Do you have two examples to show me?

    Thanks
     
    nycmathguy, Jun 8, 2022
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  2. nycmathguy

    MathLover1

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    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




    .
     
    MathLover1, Jun 8, 2022
    #2
    nycmathguy likes this.
  3. nycmathguy

    nycmathguy

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    Test the following for symmetry.

    1. csc x + sec x - 4 = 0

    2. tan x/(2x) - sin (2x) = 100
     
    nycmathguy, Jun 8, 2022
    #3
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