Question

I need help understanding how to solve this problem.

1. If on the unit circle C, the distance from P (1, 0) to the point T (5/13, 12/13 ) is x, determine the coordinates of the point at the indicated distance from P.
π+ x

A. (5/13, 12/13)
B. (-5/13, 12/13)
C. (5/13. -12/13)
D. (-5/13, -12/13)

Answer 1

D.

`( - (5)/(13) , - (12)/(13) )`

Step-by-step explanation:

From the given information we have :

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

and

`\sin(x) = (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) = - (5)/(13)`

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

`\sin(x + \pi) = - (12)/(13)`

The correct choice is:

`( - (5)/(13) , - (12)/(13) )`

Answer 2

• D. (-5/13, -12/13)

Step-by-step 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