Question 441412: find, to the nearest degree, the solution set of 12 sinx= 1+csc x over the domain {x/0 degrees less than or equal to x <360 degrees}
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! find, to the nearest degree, the solution set of 12 sinx= 1+csc x over the domain {x/0 degrees less than or equal to x <360 degrees}
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12 sinx= 1+csc x
12 sinx= 1+1/sinx
12 sin^2x= sinx+1
12 sin^2x-sinx-1=0
(4sinx+1)(3sinx-1)=0
4sinx+1=0
sinx=-1/4
using inverse sin key of calculator
reference angle=14.48 deg in quadrants III and IV where sin is negative
x=194.48 and 345.52 degrees
3sinx-1=0
sinx=1/3
reference angle=19.47 deg in quadrants I and II where sin is positive
x=19.47 and 160.53 degrees
solution:
x=194.48, 345.52, 19.47 and 160.53 degrees
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