Trigonometry Demystified, 2nd edition |

Stan Gibilisco |

Explanations for Quiz Answers in Chapter 2 |

1. In Fig. 2-10, we see no points in the upper-right quadrant, where both variables have positive values. That's the first quadrant. The correct choice is D. The point (-4,5) lies in the second quadrant; the point (-5,-3) lies in the third quadrant; the point (1,-6) lies in the fourth quadrant. The origin (0,0) doesn't lie in any quadrant. |

2. To find the distance of the point (-4,5) from the origin (0,0), we must square both
values, add the squares, and then take the positive square root of the result. If we call
this distance r, then
rounded off to three decimal places. The answer is B. |

3. To find the distance r of the point (-5,-3) from the origin (0,0), we
calculate
rounded off to three decimal places. The answer is D. |

4. To find the distance r of the point (1,-6) from the origin (0,0), we
calculate
rounded off to three decimal places. The answer is A. |

5. To find the distance d between the points (-4,5) and (-5,-3) in Fig. 2-10,
we must subtract the x values from each other, then subtract the y values
from each other (in the same order as we did with the x values), then square each
of those results separately, add the squares, and finally take the positive square root.
We calculate
rounded off to three decimal places. The correct choice is C. |

6. To find the distance d between the points (-5,-3) and (1,-6), we calculate
rounded off to three decimal places. The correct choice is C. |

7. To find the distance d between the points (1,-6) and (-4,5), we calculate
rounded off to three decimal places. The correct choice is B. |

8. To find the midpoint of a line segment in the Cartesian plane, we average the x
values of the end-point coordinates to get the x value of the midpoint; then we
average the y values of the end-point coordinates to get the y value of
the midpoint. In Fig. 2-11, the end-point coordinates for line segment L are
(-4,5) and (-5,-3). When we average the x values of the end points, we get
= (-4 - 5) / 2 = -9/2 When we average the
= (5 - 3) / 2 = 2/2 = 1 The coordinates of the midpoint are therefore ( y) = (-9/2,1)_{m}The correct choice is C. |

9. In Fig. 2-11, the end-point coordinates for line segment M are
(-5,-3) and (1,-6). When we average the x values, we get
= -4/2 = -2 When we average the
= (-3 - 6) / 2 = -9/2 The coordinates of the midpoint are therefore ( y) = (-2,-9/2)_{m}The correct choice is A. |

10. In Fig. 2-11, the end-point coordinates for line segment N are
(1,-6) and (-4,5). When we average the x values, we get
= (1 - 4) / 2 = -3/2 When we average the
= -1/2 The coordinates of the midpoint are therefore ( y) = (-3/2,-1/2)_{m}The correct choice is A. |