Question

Solve for t, 0 ≤ t < 2π

24sin^2(t) = 6tan(t)cos(t)

Thank you!

Answer 1

t ∈ {0, 0.252680, 2.888912, 3.141593}

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}