Explanation:
Consider the following expression:
[tex]\cos(x)=\frac{5}{13}[/tex]
this expression can be represented in the following right triangle:
To find y, we can apply the Pythagoras theorem as this:
[tex]y=\sqrt{13^2\text{ - 5}^2}\text{ = 12}[/tex]
but since x terminates in quadrant IV, we have that
[tex]y=\text{ - 12}[/tex]
and thus
[tex]\sin(x)=\text{ -}\frac{12}{13}[/tex]
and
[tex]\tan(x)=\text{ -}\frac{12}{5}[/tex]
now, using this data in the following formulas:
we can conclude that the correct answer is:
Answer:
[tex]\sin(2x)=\text{ -}\frac{120}{169}[/tex][tex]\cos(2x)=\text{ - }\frac{119}{169}[/tex][tex]tan(x)=\frac{120}{119}[/tex]
