Solve 12 cos^2(w)+14sin(w)-16=0 for all solutions 0 ≤ w <2𝝅

Question

Anobody know how to solve this equation?

Give your answers to 2 decimal places, as a list separated by commas.

(It should be 4 answers)

Answer 1

Divide by 2 to get 6cos²w + 7sinw - 8 = 0

6(1 - sin²w) + 7sinw - 8 = 0

-6sin²w + 7sinw - 2 = 0

6sin²w - 7sinw + 2 = 0

(3sinw - 2)(2sinw - 1) = 0

sinw = 2/3 or sinw = 1/2

If sinw = 1/2, then w = π/6 or 5π/6

Use your calculator to find the 2 solutions for the other equation.