Question

Given that cosθ= 5/13 and that θ lies in Quadrant IV, what is the exact value of sin 2θ? Answers: /?f=%5Cfrac%7B120%7D%7B169%7D" id="TexFormula1" title="\frac{120}{169}" alt="\frac{120}{169}" align="absmiddle" class="latex-formula"> $\frac{24}{13}$ - $\frac{24}{13}$ - $\frac{120}{169}$

Answer 1

Answer:

$-\frac{120}{169}$

Step-by-step explanation:

Given

$cos\theta=\frac{5}{13},-\frac{3\pi}{2}$

Use identities

$sin(2\theta)=2sin\theta cos\theta\\\\sin(2\theta)=2(-\frac{12}{13})(\frac{5}{13})\\ \\sin(2\theta)=2(-\frac{60}{169})\\ \\sin(2\theta)=-\frac{120}{169}$