Question

Solve for t, 0 ≤ t < 2π 24sin^2(t) = 6tan(t)cos(t) Thank you!

Answer 1

Answer:

  t ∈ {0, 0.252680, 2.888912, 3.141593}

Step-by-step explanation:

Simplify and factor.

  4sin(t)^2 -sin(t) = 0 . . . . use tan=sin/cos, subtract 6sin(t), divide by 6

  sin(t)(4sin(t) -1) = 0 . . . . factor

Solutions make the factors zero.

  sin(t) = 0   ⇒   t = 0, π

  4sin(t) -1 = 0   ⇒   t = arcsin(1/4), π-arcsin(1/4) ≈ 0.252680, 2.888912

  t ∈ {0, 0.252680, 2.888912, 3.141593}