Please help me!

Question

Find all angles, o≤θ<360, that satisfy the equation below, to the nearest 10th of a degree.

-4 tan² θ - 9 tan θ - 2= 0

Answer 1

Hailey:

Let x = tan(Θ)

We need to solve the following equation:

-4x²-9x-2=0 or 4x²+9x+2 = 0 (4x+1)*(x+2) = 0

So x = -2 or x = -1/4

tan(θ) = -2 or tan(θ) = -1/4

θ = tan^-1(-2) or θ=tan^-1(-1/4)

θ = -63.4 or θ = -14.04

Remember, we are looking at 0≤θ≤360

So θ = 360-63.4 = 296.6 or θ = 345.96. See if you can find any other values!

Let me know if you need extra help!