Question

If tan θ = - \sqrt(3)/3 and cos θ > 0; Find csc θ.

Answer 1

let $\theta$ = k

Now, tan k = - ($\sqrt3$ / 3) = - (1/$\sqrt3$ )

cos k > 0

Now tan k is negative when k lies in second or fourth quadrant. And cos k is positive in first and fourth quadrant.

So we can infer that k lies in the fourth quadrant.

Now tan k = - (1/$\sqrt3$ ) => k = - 30$\degree$ => k = (360 - 30)$\degree$ = 330$\degree$

So k = 330$\degree$

Now cosec k = cosec 330$\degree$ = cosec (360 - 30)$\degree$ = - cosec 30$\degree$ = -2

therefore the answer is -2.