SOLUTION: Find all solutions if 0° &#8804; &#952; < 360°. When necessary, round your answers to the nearest tenth of a degree. (Enter your answers as a comma-separated list.) sin^2 2&#952

Algebra ->  Trigonometry-basics -> SOLUTION: Find all solutions if 0° &#8804; &#952; < 360°. When necessary, round your answers to the nearest tenth of a degree. (Enter your answers as a comma-separated list.) sin^2 2&#952      Log On


   



Question 970181: Find all solutions if 0° ≤ θ < 360°. When necessary, round your answers to the nearest tenth of a degree. (Enter your answers as a comma-separated list.)
sin^2 2θ − 7 sin 2θ − 1 = 0

Answer by lwsshak3(11628) About Me  (Show Source):
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Find all solutions if 0° ≤ θ < 360°. When necessary, round your answers to the nearest tenth of a degree. (Enter your answers as a comma-separated list.)
sin^2 2θ − 7 sin 2θ − 1 = 0
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sin^2 2θ − 7 sin 2θ − 1 = 0
solve for sin 2θ by quadratic formula:
sin+2%26%23952%3B+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=1, b=-7, c=-1
ans:
sin 2θ=7.14 (reject, (-1 < sin 2θ < 1))
or
sin 2θ=-0.14
2θ=188.1˚, 352.0˚ (in quadrants III and IV where sin<0)
θ=94.0˚, 176.0˚