Solve for t, 0 ≤ t < 2π

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

Thank you!

  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}

1 is c

2 is a

3 is a

step-by-step explanation:

b is 38 degrees.

a is 52 degrees.

this is because if b is 38 and a is 14 degrees more than b than 38+14=52 and 52+38=90 degrees. hope this .