Question

Suppose that the terminal point determined by t is the point 12 13 , 5 13 on the unit circle. Find the terminal point determined by each of the following. (a) π − t (x, y) = (b) −t (x, y) = (c) π + t (x, y) = (d) 2π + t (x, y)

Answer 1

Answer:

  (a)  (-12/13, 5/13)

  (b)  (12/13, -5/13)

  (c)  (-12/13, -5/13)

  (d)  (12/13, 5/13)

Step-by-step explanation:

(a) The terminal point is effectively reflected across the y-axis, so the sign of the x-coordinate changes. (-12/13, 5/13)

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(b) The terminal point is effectively reflected across the x-axis, so the sign of the y-coordinate changes. (12/13, -5/13)

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(c) The terminal point is effectively reflected across the origin, so the signs of both coordinates change. (-12/13, -5/13)

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(d) The terminal point is mapped to itself, so its coordinates remain unchanged. (12/13, 5/13)