Thread: Quick trig problem...

I'm just doing this question that says:

Solve for Θ to the nearest hundredth, where 0 ≤ Θ ≤ 2π

3tan²Θ - 2tanΘ = 1

The answers are π/4, 2.82, 5π/4, and 5.96

I don't know how they got 2.82, or 5.96

I factored (3tanΘ+1)(tanΘ-1)
tanΘ = 1
then I used the special triangles, in the first and third quadrant to get π/4, and 5π/4.

what do I do about
tanΘ = -1/3?

Originally Posted by lanvin

I'm just doing this question that says:

Solve for Θ to the nearest hundredth, where 0 ≤ Θ ≤ 2π

3tan²Θ - 2tanΘ = 1

The answers are π/4, 2.82, 5π/4, and 5.96

I don't know how they got 2.82, or 5.96

I factored (3tanΘ+1)(tanΘ-1)
tanΘ = 1
then I used the special triangles, in the first and third quadrant to get π/4, and 5π/4.

what do I do about
tanΘ = -1/3?

Hi

You have to use Arctan function
Arctan(-1/3) = -0.32 rad
To find the answers between 0 and 2π, you just have to add π (which gives 2.82 rad) and again π (which gives 5.96 rad) because tan is a π-periodic function