Solving First Quadrant

By Author: Pierce Brosnan
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Introduction

A quadrant is an instrument,if used to measure angles up to 90°. It was originally propose by Ptolemy as a better kind of astrolabe Several different variations of the instrument were later produced by medieval Muslim astronomers.

The geometric quadrant is a quarter, if circle panel usually of wood Markings on the surface might be printed on paper and pasted to the wood directly on the surface. Brass instruments had their markings scribed directly in to the brass

type of quadrant

1. The sine quadrant also known as the Sine cal Quadrant was used for solving trigonometric problems and taking astronomical observations. It was developed by all Khwarizmi in 9th century Baghdad and prevalent until the nineteenth century. Its defining feature is a graph paper like grade if one side that is divided into sixty equal intervals on each axis and is also bounded by a 90 degree graduated arc. A cord was attached to the apex of the quadrant with in bead at the end of it to act as a plumb bob. They were also sometimes drawn on the back of astrolabes.

2. The universal quadrant used ...
... for solving astronomical problems for any latitude. These quadrants had either one or two sets of Shakespeare grids and were developed in the fourteenth century in Syria. Some astrolabes are all so printed on the back with the universal quadrant like an astrolabe created by IbnalSarrāj.

3. The hoary quadrant used for finding the time with the sun. The hoary quadrant to be find the time is either equaled or unequal a hours. Different sets of markings were created for either equal or unequal hours. For measuring the time in equal hours, the hoary quadrant could only be used for one specific latitude while a quadrant for unequal hours could be used anywhere based on an approximate formula. One edge of the quadrant had to be aligned with the sun and one aligned, a bead on the end of a plumb line attached to the center of the quadrant showed the time of the day.

4. The astrolabe alimentary quadrant a quadrant developed to the astrolabe. This quadrant make with a one half of a typical astrolabe plate. if astrolabe plates are symmetrical. A cord attached from the center of the quadrant with a bead at the other end was moved to represent the position of a celestial body . The ecliptic and star positions were make on the quadrant for the above. It is not known where and when the astrolabe quadrant was invented,if existent astrolabe quadrants are either of Ottoman or Mameluke origin, while there have been discovered twelfth century Egyptian and fourteenth century Syrian treatises on the astrolabe quadrant. These quadrants proved to be very popular alternative of astrolabes.

Examples

Example1:
In which quadrants signs of both the x and y coordinates of the point is same?

A ) second and third quadrants
B ) first and fourth quadrants
C ) first and third quadrants
D ) first and second quadrants

Steps to derive

1 In the first quadrant, the signs of both the x and y coordinates are positive.

2 In the second quadrant the x-coordinate is negative,than y coordinate is positive.

3 In the third quadrant, both the x and y coordinates are negative.

4 In the fourth quadrant, x coordinate is positive and the y-coordinate is negative.

5 So, the signs of both the x and y coordinates point are the same in the first and third quadrants.

answer is Option C

Example2:
Solve x2 + 6x – 7 = 0 by completing the square.

solution

x2 + 6x – 7 = 0
(x + 3)2 = 16
x + 3 = ± 4
x = – 3 ± 4
= – 3 – 4, –3 + 4
= –7, +1

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