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 1098979: 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 − 5 sin 2θ − 1 = 0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use a substitution,
u=sin%282%2Atheta%29
Then,
u%5E2-5u-1=0
Complete the square,
u%5E2-5u%2B%285%2F2%29%5E2-1=%285%2F2%29%5E2
%28u%2B5%2F2%29%5E2=25%2F4%2B4%2F4
%28u%2B5%2F2%29%5E2=29%2F4
u%2B5%2F2=0+%2B-+sqrt%2829%29%2F2
u=-5%2F2+%2B-+sqrt%2829%29%2F2
Only one solution is valid since -5%2F2-sqrt%2829%2F2%29%3C-1.
sin%282%2Atheta%29=-5%2F2%2Bsqrt%2829%29%2F2
sin%282%2Atheta%29=-0.19258
Two solutions,
theta=95.6 and
theta=174.5