Question

I have an online quiz but I cant do this two excersise 1) The following is the smallest solution to the equation -12sin2(x) - 11cos(x) + 14 = 0 in the range [0,2π). Express your answer in radians 2)The following is the smallest solution to the equation 13cos(x) = -5.5 + 7.5cos(2x) in the range [0,2π). Express your answer in radians

Answer 1

\[-12\sin^2(x) - 11\cos(x) + 14 = 0\] start with the fact that \(\sin^2(x)=1-\cos^2(x)\) to get
\[-12(1-\cos^2(x) )- 11\cos(x) + 14 = 0\] and then get a quadratic equation in \(\cos(x)\)

Answer 2

i.e. solve
\[12\cos^2(x)-11\cos(x)+2=0\]

Answer 3

but how can I express that in radians? because the anwers is 0.8411