SOLUTION: find all solutions if 0_< theta < 360 sin^2(2)x - 4sin2x - 1 = 0

Algebra ->  Trigonometry-basics -> SOLUTION: find all solutions if 0_< theta < 360 sin^2(2)x - 4sin2x - 1 = 0      Log On


   

Question 679509: find all solutions if
0_< theta < 360
sin^2(2)x - 4sin2x - 1 = 0
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
find all solutions if
0_< theta < 360
sin^2(2)x - 4sin2x - 1 = 0
solve for sin(2x) using following quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=1, b=-4, c=-1
ans:
sin(2x)=4.236 (reject, -1 ≤ sin(2x) ≤ 1)
or
sin(2x)≈-0.236
2x≈193.65º and 346.35º (in quadrants III and IV where sin<0
x=96.82º and 173.18º