1 Answer

Feofilakt · Answer 1 · 2023-12-13T05:47:52+0000

Step-by-step explanation:

Consider the following expression:

$\cos(x)=(5)/(13)$

this expression can be represented in the following right triangle:

To find y, we can apply the Pythagoras theorem as this:

$y=\sqrt{13^2\text{ - 5}^2}\text{ = 12}$

but since x terminates in quadrant IV, we have that

$y=\text{ - 12}$

and thus

$\sin(x)=\text{ -}(12)/(13)$

and

$\tan(x)=\text{ -}(12)/(5)$

now, using this data in the following formulas:

we can conclude that the correct answer is:

$\sin(2x)=\text{ -}(120)/(169)$
$\cos(2x)=\text{ - }(119)/(169)$
tan(x)=(120)/(119)