SOLUTION: Find approximate solutions of the given equation 5sin^2 (x) - sin (x) - 2 = 0 thank you!

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Question 1053562: Find approximate solutions of the given equation
5sin^2 (x) - sin (x) - 2 = 0
thank you!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +z+=+sin%28x%29+
+5%2A%28sin%28x%29%29%5E2+-+sin%28x%29+-+2+=+0+
+5z%5E2+-+z+-+2+=+0+
Use quadratic formula
+z+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+5+
+b+=+-1+
+c+=+-2+
+z+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2+-+4%2A5%2A%28-2%29+%29%29%2F%282%2A5%29+
+z+=+%28+1+%2B-+sqrt%28+1+%2B+40+%29%29%2F10+
+z+=+%28+1+%2B-+6.4031+%29+%2F+10+
+z+=+7.4031%2F10+
+z+=+.7403+
and
+z+=+-5.4031%2F10+
+z+=+-.5403+
-------------------------
+sin%28x%29+=+.7403+
+x+=+arc+sin%28+.7403+%29+
+x+=+47.757+ degrees
and
+x+=+arc+sin%28+-.5403+%29+
+x+=+-32.704+ degrees
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Aso for +x+, I get:
+x+=+180+-+47.757+
+x+=+132.243+
( this is 2nd quadrant where sin is also positive )
and
+x+=+-180+-%28+-32.704+%29+
+x+=+-180+%2B+32.704+
+x+=+-147.296+
( this is 3rd quadrant where sin is also negative )
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