Angles & Degree Measure-Scribe Post-Moboss

Hey Guys,
We have began a new Chapter-Angles & Trigonometric Functions. In this post I will cover basic definitions and will provide you with examples.

ANGLES
Angles are made up of a couple of elements:
- Angles: Defined as union of two rays with a common endpoint.
- Ray: Defined as a point on a line together with all points of the line on one side of that point.
- Vertex: Two rays with a common endpoint.
- Initial Side: The fixed side of a ray.
- Terminal Side: The rotating side of a ray.
- Central Angle: Angle whose vertex is the center of a circle.
- Intercepted Arc: Arc of circle through which the terminal side moves.
- Standard Position: Angle in a rectangular coordinate system with a vertex in the origin and the initial side is the positive x-axis.

DEGREE MEASURE OF AN ANGLE
- Degree measure of an angle: Number of degrees in the intercepted arc of a circle centered at the vertex. The degree measure is positive if the rotation is counter clockwise and negative if the rotation is clockwise.

TYPES OF ANGLES
- Obtuse Angle: Angle between 90 degrees and 180 degrees.
- Acute Angle: Angle between 0 degrees and 90 degrees.
- Straight Angle: Angle exactly 180 degrees.
- Right Angle: Angle exactly 90 degrees.
- Quadrantal Angle: Angle whose terminal side is on an axis.

TO BE COTERMINAL OR NOT TO BE?
- Coterminal Angle: Has the same terminal side. Degree measures of the coterminal angles differ by a multiple of 360 degrees (one complete revolution).
- Coterminal Angles: Angles that are on the same Quadrant.
- Formula for finding Coterminal Angles:

- Example:
Find two positive angles and two negative angles that are coterminal with -50 degrees.

Solution
Simply choose two positive integers and two negative integers for the K in the formula

. I will be using 1 & 2 for the positive integers. I will be using -1 & -2 for the negative integers.

Angles:

are coterminal with-50 degrees.

DETERMINING IN WHICH QUADRANT AN ANGLE LIES



- To determine the quadrant in which an angle lies, add or subtract multiples of (one revolution) to obtain a coterminal angle with a measure between 0 degrees and .
** Take the original number and either add or subtract according to whether the original number is positive or negative. When adding or subtracting the number of rotation add or subtract so that the solution is between 0 degrees and 360 degrees**
- Example:

, this means that -580 degrees is in the 3rd Quadrant.

Next Scribe Jericho.

M