Pre-cal trigonometric equation problemam i correct to factor out a 2 first? 2 sin 2 ⁡ 2 x = 1 2 ( sin 2 ⁡ x − 1 ) = 1 2 cos 2 ⁡ x = 1 cos 2 ⁡ x = 1 2 cos ⁡ x = ± 2 2 i'm only looking for solutions from 0 ≤ x ≤ 2 π x = π 4 , 7 π 4 , 3 π 4 , 5 π 4 thanks for any corrections

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Pre-cal trigonometric equation problemam i correct to factor out a 2 first?  2      sin    2    ⁡  2  x  =  1  2  (      sin    2    ⁡  x  −  1  )  =  1  2      cos    2    ⁡  x  =  1      cos    2    ⁡  x  =            1      2        cos  ⁡  x  =  ±                    2            2      i&#039;m only looking for solutions from  0  ≤  x  ≤  2  π  x  =            π      4        ,                    7        π            4        ,                    3        π            4        ,                    5        π            4      thanks for any corrections

iletsa2ym · Accepted Answer

Hint: let   y  =  sin  ⁡  2  x and solve for   y first using algebra. Then figure out what value(s) of   x would make the equation true.

Davirnoilc · Accepted Answer

2                  sin          2                ⁡        (        2        x        )        =        1                            ⇒                    2                  (                                    1              −              cos              ⁡              (              4              x              )                        2                    )                =        1                            ⇒                    1        −        cos        ⁡        (        4        x        )        =        1                            ⇒                    cos        ⁡        (        4        x        )        =        0                            ⇒                    4        x        =                              n            π                    2                ,                n        ∈        {        1        ,        3        ,        5        ,        7        ,        …        }                            ⇒                    x        =                              n            π                    8                ,        n        ∈        {        1        ,        3        ,        5        ,        7        ,        …        }            Hence the set is  x  ∈      {          π      8        ,                  3        π            8        ,                  5        π            8        ,    …    }

Pre-cal trigonometric equation problem am i correct to factor out a 2 first? 2sin^2 2x=1 2(sin^2 x−1)=1 2cos^2 x=1 cos^2 x=1/2

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