I am really stuck with this question

Given that $cosec\theta = -\sqrt 2$

and $tan \theta = -1$

and $-\pi<0<\pi$

find the exact value of $\theta$ in radians. Justify your answer.

I keep trying to find the relationship by rearranging $cosec$ in terms of $cot$ and then $tan$ but i'm not making any headway.

I feel like I'm missing something really obvious. Can anyone point me in the right direction??

Thanks

2. Originally Posted by Ian1779
Given that $\csc\theta = -\sqrt{2}$

and $\tan(\theta) = -1$ and $-\pi\, <\, 0\, <\,\pi$

find the exact value of $\theta$ in radians. Justify your answer.
The cosecant is the reciprocal of the sine, so the above is saying that the sine is negative, so you're in Quadrant III or Quadrant IV. Also, the tangent is negative, so you're in... what Quadrant?

You have memorized the basic reference angle values, so you know the reference angle for $\tan(\theta)\, =\, 1$, and thus for $\tan(\theta)\, =\, -1$.

So what must $\theta$ be...?