Question 1011901: please help me solve this equation: solve exactly: sin(x) + 4csc(x) + 5=0
I have done: sin(x) + 4/sin(x) +5=0
sin^2(x)/sin(x)+4/sin(x)+5+0
4+sin^2(x)/sin(x)=-5
4+sin^2(x)=-5sin(x)
sin^2(x)+5sin(x)+4=0
(sin(x)+1) (sin(x)+4) =0
sin(x)=-1, sin(x)=-4.
Please let me know if I have made a mistake somewhere, and/or where to go from here. I need to have an exact value, so I can't just plug in sin^-1(-1) and sin^-1(-4) into my calculator.
Thanks so much
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! solve exactly:
sin(x) + 4csc(x) + 5=0
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Multiply thru by sin(x) to get:
sin^2(x) + 5sin(x) + 4 = 0
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Factor:
(sin(x)+1)(sin(x)+4) = 0
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sin(x) = -1 or sin(x) = -4 (extraneous)
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sin(x) = -1 when x = 270 degrees.
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Cheers,
Stan H.
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