Question

Find all solutions on the interval [0, 2π).

Look for opportunities to use trigonometric identities. (Enter your answers as a comma-separated list. Round your answers to four decimal places. If an answer does not exist, enter DNE.)


$12sin^2(t)+cos(t)-3=3$


I got t= 0, $cos^-1(\frac{3}{4} )$, $cos^-1(\frac{-2}{3})$ but not sure if they're correct

Answer 1

Answer:

t = 0.7227, 2.3005, 3.9827, 5.5605

Step-by-step explanation:

12(1 - cos²t) + cost - 3 - 3 = 0

-12cos²t + cost + 6 = 0

-12cos²t +9cost - 8cost + 6 = 0

-3cost(4cost - 3) - 2(4cost - 3) = 0

(4cost - 3)(-3cost - 2) = 0

cost = ¾ cost = -⅔

t = (cos^-1)(3/4)

t = 0.7227, 5.5605

t = (cos^-1)(-2/3)

t = 2.3005, 3.9827