Question

Find sin 2x, cos 2x, and tan 2x if cosx= 5/13 and x terminates in quadrant IV.

Answer 1

Explanation:

Consider the following expression:

$\cos(x)=\frac{5}{13}$

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

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

and

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

now, using this data in the following formulas:

we can conclude that the correct answer is:

Answer:

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