9cos(t)+30cos^2(t)-3=0

Question

Find all solutions to the equation below in the interval [0,2π). Give all answers as decimals rounded to 3 places

Answer 1

9cos(t)+30cos^2(t)-3=0

Let x = cos(t). This gives us:

30x² + 9x - 3 = 0

10x² + 3x - 1 = 0

(5x - 1)(2x + 1) = 0

x = 1/5, -1/2

t = acos(1/5) = 1.37 radians

t = acos(-1/2) = 2.09 radians

There are 2 more solutions at the negative of those angles. (convert negative angles to positive by adding 2pi)