Question

Use the given information to determine the exact trigonometric value. (in the image attached)

Answer 1

Answer:

OPTION B: $\frac{-2\sqrt{5}}{5}$

Step-by-step explanation:

Given $cot \theta = -\frac{\sqrt{5}}{2}$

We know that, $\frac{1}{cot \theta} = tan \theta$

$\implies tan \theta = \frac{1}{-\frac{\sqrt{5}}{2}}$

$= -\frac{2}{\sqrt{5}}$

Multiplying and dividing by $\sqrt{5}$, we get:

$tan \theta = - \frac{2 \sqrt{5}}{\sqrt{5}\times \sqrt{5}}}$

$\implies tan \theta = -\frac{2\sqrt{5}}{5}$

Hence, OPTION B is the answer.