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Math Help - solve 2sin(x-45)=1

  1. #1
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    solve 2sin(x-45)=1

    Solve the equation 2sin(x-45^0) = 1 for 0^0<x<360^0
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  2. #2
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    Just work your way backwards:

    2\sin(x-45^{\circ}) = 1

    \sin(x-45^{\circ}) = \frac{1}{2}

    x-45^{\circ} = \sin^{-1}\left(\frac{1}{2}\right)

    Can you carry on?
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  3. #3
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    Solve it the way you normally would

    2\sin{(x - 45^{\circ})} = 1

    \sin{(x - 45^{\circ})} = \frac{1}{2}

    x - 45^{\circ} = \left\{30^{\circ}, 180^{\circ} - 30^{\circ}\right\}

    x - 45^{\circ} = \left\{30^{\circ}, 150^{\circ}\right\}

    x = \left\{30^{\circ} + 45^{\circ}, 150^{\circ} + 45^{\circ}\right\}

    x = \left\{75^{\circ}, 195^{\circ}\right\}.
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