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Time Period of SinX

Time Period of SinX and Sin 120

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Time Period of Sinx

Time period of Sin(x) Sin(120º - x) Sin(120º + x)

= Sinx { Sin2120º Cos2x – Cos2120º Sin2x}
= Sinx {(Sin(90º + 30º)2 Cos2x –  (Cos(90º + 30º)2 Sin2x}
= Sin {Cos2 30º Cos2x – Sin2 30º Sin2x}
= Sinx {3/4 Cos2x – 1/4 Sin2x}
= Sinx {3(1-Sin2x)/4 – 1/4Sin2x}
= Sinx {3/4 – 4/4 Sin2x}
= 14 {3Sinx – 4Sin3x}
= Sin3x/4
Therefore, Sinx = 2π
Sin3x = 2π/3
Sin(x) Sin(120º - x) Sin(120º + x) = 2π

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