Trigonometric EquationGiven the function 2 sin ⁡ ( 2 x + π 2 ) find the amplitude, the period, the phase shift and the intersection points with the parent function, sin ⁡ ( x )I was able to find the characteristics:Period: πAmplitude: 2Phase shift: π 4 However I couldn't solve the equation 2 sin ⁡ ( 2 x + π 2 ) = sin ⁡ ( x ). My difficulty was those factors that multiply the sine and the variabel.

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Trigonometric EquationGiven the function   2  sin  ⁡  (  2  x  +      π    2    ) find the amplitude, the period, the phase shift and the intersection points with the parent function,   sin  ⁡  (  x  )I was able to find the characteristics:Period:   πAmplitude: 2Phase shift:       π    4  However I couldn&#039;t solve the equation   2  sin  ⁡  (  2  x  +      π    2    )  =  sin  ⁡  (  x  ). My difficulty was those factors that multiply the sine and the variabel.

dobradisamgn · Accepted Answer

Using   sin  ⁡  (  a  +  b  )  =  sin  ⁡  a  cos  ⁡  b  +  sin  ⁡  b  cos  ⁡  a gives you  2  cos  ⁡  2  x  =  sin  ⁡  x  .Now, using   cos  ⁡  2  a  =  1  −  2      sin    2    ⁡  a gives  2  (  1  −  2      sin    2    ⁡  x  )  =  sin  ⁡  x  .The above can be written as  4      sin    2    ⁡  x  +  sin  ⁡  x  −  2  =  0.This is a quadratic equation in   sin  ⁡  x. By the quadratic formula:  sin  ⁡  x  =                    −        1        ±                  33                    8        .Then, for   x in the interval   [  −  π      /    2  ,  π      /    2  ]  x  =  arcsin  ⁡  (                    −        1        ±                  33                    8        )(  x  ≈  .63487 or   x  ≈  −  1.003).Both of these are solutions to the original equation   2  sin  ⁡  (  2  x  +            π      2        )  =  sin  ⁡  x.Of course, there are other solutions to find...

Trigonometric Equation Given the function 2sin(2x+pi/2) find the amplitude, the period, the phase shift and the intersection points with the parent function, sin(x)

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