Trigonometry Demystified, 2nd edition |

Stan Gibilisco |

Explanations for Quiz Answers in Chapter 1 |

1. The chapter text tells us that two triangles are directly congruent if and only if
they're directly similar and the corresponding sides have identical lengths. Direct
congruence is a special case of direct similarity. If we find two directly congruent
triangles, then we know that they're directly similar. The correct choice is B. |

2. A full circle of 360º contains 2π radians. If we consider π = 3.14159, then 2π = 6.28318, so a radian must equal 360º divided by 6.28318. That's approximately 57.3º. The correct choice is A. |

3. In Fig. 1-15, the uppermost interior angle measures π/2 rad, so it's a right angle. Therefore, we know that the figure is a right triangle. The correct choice is B. |

4. In any Euclidean triangle (any triangle on a flat surface) the measures of the
interior angles always add up to 180º. Therefore, in the situation of Fig. 1-15, we know
that x + y = 180º minus the measure of the top angle, which is π/2
rad or 90º. By simple arithmetic, x + y = 90º, so choice C works. But,
because all three angles in any triangle must have measures larger than 0º, we can deduce
that x < 90º and y < 90º, so choices A and B are also correct. The
right answer is D, "All of the above." |

5. By definition, a triangle is isosceles if and only if two of its sides have
the same length. In an equilateral triangle, all three of the sides have the same length,
so any equilateral triangle is also isosceles. The correct choice is C. |

6. The sine of any angle inside a right triangle (other than the right
angle) is always positive but less than 1. That is,θ0 < sin
Choice A represents the correct answer. |

7. The cosine of any angle θ inside a right triangle (other than the right
angle) is always positive but less than 1. That is,0 < cos
Choice A represents the correct answer. |

8. The tangent of any angle θ inside a right triangle (other than the right
angle) is always positive. Its value can equal any positive real number; no limit exists
as to how large it can get. We write this fact astan The correct choice is D. |

9. The cosecant of any angle θ inside a right triangle (other than the right
angle) equals the reciprocal of the sine of that same angle θ. Because we know
that0 < sin we can conclude that csc The correct choice is C. |

10. A complete circle contains 2π radians. The quantity π/8 equals 1/16 of 2π. Therefore, an angle of π/8 rad represents 1/16 of a full circle. The correct choice is C. |