AnthonyFleming
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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)

I need help understanding how to solve this problem1 If on the unit circle C the distance from P 1 0 to the point T 513 1213 is x determine the coordinates of t class=

Respuesta :

Edufirst

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
kudzordzifrancis

Answer:

D.

[tex]( - \frac{5}{13} , - \frac{12}{13} )[/tex]

Step-by-step explanation:

From the given information we have :

[tex] \cos(x) = \frac{5}{13} [/tex]

and

[tex] \sin(x) = \frac{12}{13} [/tex]

Now we need to find :

[tex] \cos(x + \pi) \: and \: \sin(x + \pi) [/tex]

We make use of trigonometric identities.

[tex] \cos(x + \pi) = - \cos(x) [/tex]

This implies that:

[tex]\cos(x + \pi) = - \frac{5}{13} [/tex]

[tex]\sin(x + \pi) = - \sin(x) [/tex]

[tex]\sin(x + \pi) = - \frac{12}{13} [/tex]

The correct choice is:

[tex]( - \frac{5}{13} , - \frac{12}{13} )[/tex]

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