## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 3 - Radian Measure and the Unit Circle - Section 3.2 Applications of Radian Measure - 3.2 Exercises - Page 114: 68b

#### Answer

Greenwich Mean Time (GMT) is the time in Greenwich, England which is at a longitude of $0^{\circ}$. If our time zone is ahead of GMT, then we are east of the prime meridian. If our time zone is $x$ hours ahead of GMT, that is $x$ time zones east of Greenwich, then our longitude is approximately $(15~x)^{\circ}~E$. If our time zone is behind GMT, then we are west of the prime meridian. If our time zone is $x$ hours behind GMT, that is $x$ time zones west of Greenwich, then our longitude is approximately $(15~x)^{\circ}~W$.

#### Work Step by Step

Greenwich Mean Time (GMT) is the time in Greenwich, England which is at a longitude of $0^{\circ}$. If our time zone is ahead of GMT, then we are east of the prime meridian. If our time zone is $x$ hours ahead of GMT, that is $x$ time zones east of Greenwich, then our longitude is approximately $(15~x)^{\circ}~E$. For example, New Delhi, India is 5 time zones ahead of GMT. New Delhi's longitude is approximately $(5)(15^{\circ})~E$ which is $75^{\circ}~E$. If our time zone is behind GMT, then we are west of the prime meridian. If our time zone is $x$ hours behind GMT, that is $x$ time zones west of Greenwich, then our longitude is approximately $(15~x)^{\circ}~W$. For example, Los Angeles, California is 8 time zones behind GMT. Los Angeles' longitude is approximately $(8)(15^{\circ})~W$ which is $120^{\circ}~W$.

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