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    Solve the following equations for 0 <= theta <= 360
    i) 2sin2theta = costheta - I got values for theta as 90, 270, 30, 150.
    however the answers in the book say: theta= 14.5, 90, 165.5, 270
    iii) cos2theta + sintheta = 0 - I got values for theta as 30, 150, 90, 270.
    However the book says: theta= 90, 210, 330.
    I’m not sure how the book got those answers?
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    is it 2sin 2theta or 2 sin^2 theta?
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    (Original post by brainmaster)
    is it 2sin 2theta or 2 sin^2 theta?
    2sin 2theta
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    Okay I'll show you maybe you haven't taken identified well
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    (Original post by znx)
    Solve the following equations for 0 <= theta <= 360
    i) 2sin2theta = costheta - I got values for theta as 90, 270, 30, 150.
    however the answers in the book say: theta= 14.5, 90, 165.5, 270
    \begin{aligned} 2 \sin 2 \theta = \cos \theta & \Leftrightarrow 4\sin \theta \cos \theta - \cos \theta = 0 \\ & \Leftrightarrow \cos \theta (4\sin \theta - 1) = 0\end{aligned}

    So, \cos \theta = 0 or 4\sin \theta -1= 0 and solve these.

    Do the second question similarly.
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    (Original post by RDKGames)
    \begin{aligned} 2 \sin 2 \theta = \cos \theta & \Leftrightarrow 4\sin \theta \cos \theta - \cos \theta = 0 \\ & \Leftrightarrow \cos \theta (4\sin \theta - 1) = 0\end{aligned}
    So, \cos \theta = 0 or 4\sin \theta -1= 0 and solve these.

    Do the second question similarly.
    thanks for helping, I forgot to times by 2 when changing sin2theta
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    Name:  image-171dab0f-ab42-46a4-bc50-0fecd365a0b72017334199-compressed.jpg.jpeg
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    there you go that's the way they got their answers if you don't understand a part you can ask😊
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    (Original post by brainmaster)
    there you go that's the way they got their answers if you don't understand a part you can ask😊
    First of all, you're method is somewhat flawed (at least in first image since I can't be bothered to look at the second) because you make the rookie mistake of dividing through by \cos \theta when you were supposed to factor it out instead. Then you found the correct solutions of 14.5 and 165.5 but to me it looks like you thought "Well, these are two out of four solutions mentioned, and I don't know where I'm supposed to get 90 and 270 from but I'll put them in there anyway!"

    In fact, 90 and 270 come precisely from you factoring out \cos \theta and setting it equal to 0

    Secondly, please don't post full solutions on this forum - read the posting guidelines to provide effective help.
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    (Original post by RDKGames)
    First of all, you're method is somewhat flawed (at least in first image since I can't be bothered to look at the second) because you make the rookie mistake of dividing through by \cos \theta when you were supposed to factor it out instead. Then you found the correct solutions of 14.5 and 165.5 but to me it looks like you thought "Well, these are two out of four solutions mentioned, and I don't know where I'm supposed to get 90 and 270 from but I'll put them in there anyway!"

    In fact, 90 and 270 come precisely from you factoring out \cos \theta and setting it equal to 0

    Secondly, please don't post full solutions on this forum - read the posting guidelines to provide effective help.
    thanks I'm New here so I dint know that...And yes you were right I dint know where to get the other two solutions but then I saw u could bring cos on this side and factor it later but he got the answers too so I dint bother writing it....And I'm still a rookie I haven't dealt with many trig equations but thanks for help😊
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