# Math Help - find an angle from cosec and tan

1. ## find an angle from cosec and tan

Given that cosec θ = −2, tan θ = 1/3√3 and −π < θ < π, find the exact
value of the angle θ in radians. Justify your answer.

so far i know that
sin θ = -1/2 θ = -π/6
tan θ = 1/√3 θ = π/6

from this i know that its in the third quadrant, does this mean the angle in radians im looking for is π/6?

any help would be great, thanks!

2. ## Re: find an angle from cosec and tan

Originally Posted by gurnster76
Given that cosec θ = −2, tan θ = 1/3√3 and −π < θ < π, find the exact
value of the angle θ in radians. Justify your answer.

so far i know that
sin θ = -1/2 θ = -π/6
tan θ = 1/√3 θ = π/6

from this i know that its in the third quadrant, does this mean the angle in radians im looking for is π/6?

any help would be great, thanks!
Yes. Solution of first eq. is $-\frac{\pi}{6}$ and solution of second eq. is $\frac{\pi}{6}$.

3. ## Re: find an angle from cosec and tan

im asked to find the exact value, my question is; as its in the third quadrant is the answer π/6 not -π/6?

4. ## Re: find an angle from cosec and tan

Originally Posted by gurnster76
Given that cosec θ = −2, tan θ = 1/3√3 and −π < θ < π, find the exact
value of the angle θ in radians. Justify your answer.

so far i know that
sin θ = -1/2 θ = -π/6
tan θ = 1/√3 θ = π/6

from this i know that its in the third quadrant, does this mean the angle in radians im looking for is π/6?
to satisfy both of the given ratios in the given interval ...

$\theta = -\frac{5\pi}{6}$