Question 960652
Solving the following equation will require you to use the quadratic formula. Solve the equation for θ between 0° and 360°, and round your answers to the nearest tenth of a degree. (Enter your answers as a comma-separated list.)
4 cos2 θ + 5 sin θ − 1 = 0
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4 cos2 θ + 5 sin θ − 1 = 0
4(1-sin^2x)+5sinx-1=0
4-4sin^2x+5sinx-1=0
-4sin^2x+5sinx+3=0
4sin^2x-5sinx-3=0
let u=sinx
sin^2x=u^2
..
4 u^2-5u-3=0
{{{u = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
a=4, b=-5, c=-3
ans:
u=-0.443=sinx
sinx=-0.443
x=206.3˚, 333.7˚
or
u=1.693
sinx=1.693 (no solution)(-1 ≤ sinx ≤ 1)