Today is our topic of discussion Angles in Geometry and in Trigonometry .
Angles in Geometry and in Trigonometry
For the convenience of discussion of angles in geometry and trigonometry, let us draw a pair of mutually perpendicular straight lines XOX’ and YOY’ at the plane XY.In the following figure as the lines bisects at the point O, each of the regions included between the four right-angles is called a Quadrant. By moving anti- clockwise from the line OX, the first region enclosed by (∠XOY 1 right angle) is called First quadrant and by moving accordingly region enclosed by second (ZYOX’), third (∠X’OY’) and fourth (∠XOY’)right angles are called second, third and fourth quadrant (Following figure).
In geometry angle is formed by two rays meeting at a point. In trigonometry an angle is produced by a revolving ray about a fixed ray. Let, OA is a revolving ray and at the beginning it revolve anticlockwise from the fixed ray OX.
The ray OA at first form acute angle ∠XOA₁ at the position OA, and remain in the first quadrant and then when it come to the position perpendicular to OY with OX, the measurement of ZXOY become 90° or 1 right angle. By more revolving at the same direction when the ray OA comes to the position OA2, then it forms an obtuse angle ∠XOA2. By more revolving at same direction when the ray OA comes to the opposite of the ray OX at the position of OX’, then the angle ∠XOX’ is formed is a straight angle or 2 right angle.
By complete revolving when the ray OA comes to previous position that is merge with OX, then the angle formed is 2 straight angle or 4 right angle. In geometry angles are limited to 180°, and there is no difference between geometric and trigonometric angles in this case.
If we consider that the ray OA revolves further to reach OA₁ after completing a round then the angle formed XOA₁ becomes greater than 4 right angles. The angle ∠XOX created by the original position of the ray OA is not considered as a geometric angle, but it is considered an angle in trigonometry.
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