SOLUTION: Find all solutions on [0, 2𝜋). (Enter your answers as a comma-separated list. Round your answers to four decimal places.) 12 sin^2(x) + 8 sin(x) + 1 = 0

Algebra ->  Trigonometry-basics -> SOLUTION: Find all solutions on [0, 2𝜋). (Enter your answers as a comma-separated list. Round your answers to four decimal places.) 12 sin^2(x) + 8 sin(x) + 1 = 0      Log On


   

Question 1203696: Find all solutions on
[0, 2𝜋). (Enter your answers as a comma-separated list. Round your answers to four decimal places.)
12 sin^2(x) + 8 sin(x) + 1 = 0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Find all solutions on
[+0, +2pi). (Enter your answers as a comma-separated list. Round your answers to four decimal places.)

+12sin%5E2%28x%29+%2B+8sin%28x%29+%2B+1+=+0....factor
+12sin%5E2%28x%29+%2B2sin%28x%29+%2B+6sin%28x%29%2B+1=0
+%2812sin%5E2%28x%29+%2B2sin%28x%29%29+%2B+%286sin%28x%29%2B+1%29=0
2+sin%28x%29%286sin%28x%29+%2B1%29+%2B+%286sin%28x%29%2B+1%29=0
+%282sin%28x%29+%2B+1%29+%286sin%28x%29+%2B+1%29=0

solutions:

+2sin%28x%29+%2B+1=0 => sin%28x%29+=-1%2F2
+x+=+%281%2F6%29+%2812pi%2A+n+%2B+pi%29, +n element++Z
+x+=+%281%2F6%29+%2812pi%2A+n+-+pi%29,++n+element++Z
or
+6sin%28x%29+%2B+1=0=> sin%28x%29+=-1%2F6
+x+=+2+pi%2A+n+%2Bsin%5E%28-1%29%281%2F6%29, +n+element +Z
+x+=+2+pi%2A+n+-+sin%5E%28-1%29%281%2F6%29, +n element +Z


solutions on [+0,++2pi):

+x++=++pi+%2Bsin%5E%28-1%29%281%2F6%29 or x=pi%2B0.16744
+x+=+-+sin%5E%28-1%29%281%2F6%29+ or x=-0.16744%2B2pi
+x=7pi%2F6
+x=11pi%2F6

Round your answers to four decimal places
+x+=++3.3090+
+x+=+6.1157
+x=3.6652
+x=5.7596

x={ +3.3090,3.6652,5.7596,6.1157 }