Question

I need help understanding how to solve this problem.

Answer 1

Answer:

D.

$( - \frac{5}{13} , - \frac{12}{13} )$

Step-by-step explanation:

From the given information we have :

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

and

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

Now we need to find :

$\cos(x + \pi) \: and \: \sin(x + \pi)$

We make use of trigonometric identities.

$\cos(x + \pi) = - \cos(x)$

This implies that:

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

$\sin(x + \pi) = - \sin(x)$

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

The correct choice is:

$( - \frac{5}{13} , - \frac{12}{13} )$

Answer 2

Answer:

• D. (-5/13, -12/13)

Explanation:

It is indicated to find the coordinates of the point T (5/13, 12/13) at a distance π + x.

• π is an arc of half a circle, i.e. 180º.

Then, the distance π+ x means that the point T is rotated 180º.

The rule for the rotation of a point 180º around the origin is:

• (x, y) → (-x, - y)

Applying that rule to the point T:

• (5/13, 12/13) → (-5/13, - 12/13) ← answer