Question

If $\tan\theta = \frac{- 4}{3},$ then$\sin\theta =$

• A. – 4/5 but not 4/5
• B. – 4/5 or 4/5
• C. 4/5 but not – 4/5
• D. None of these

Answer 1

Answer: (B)

– 4/5 or 4/5

Answer 2

Since $\text{cose}\text{c}^{2}\theta = 1 + \cot^{2}\theta = 1 + \frac{9}{16} = \frac{25}{16}$ $\left( \because\tan\theta = - \frac{4}{3} \right)$

$\sin^{2}\theta = \frac{1}{\text{cose}\text{c}^{2}\theta} = \frac{16}{25} \Rightarrow \sin\theta = \pm \frac{4}{5},$

Both the values are acceptable, since $\tan\theta = - \frac{4}{3}$

$i.e.,\theta$ lies in $2^{nd}$or $4^{th}$quadrant.