The point cap p times open paren x comma y close paren is on the terminal ray of angle theta If theta is between pi radians and 3 pi over 2 radians and cosecant theta is equal to negative 5 halves , what are the coordinates of cap p times open paren x comma y close paren ?

Since cosecant θ = −5/2, sine θ = −2/5. In quadrant III, both x and y are negative, and sine equals y/r, where r = √(x² + y²). Choice B has x = −√21 and y = −2, giving r = √(21 + 4) = 5 and y/r = −2/5, so the coordinates are (−√21, −2).

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