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Angles And Their Measurements

The angle is a structure formed with the help of two rays by sharing a common endpoint known as vertex of the angle. There are also trig identities which involves the angles and their measurements. The Trigonometric Identities are separated from the triangle properties, which involve both the angles and sides of the triangle. These identities are helpful in resolving the Functions and also when trig Functions need to be simplified.

The major functions are sine, cosine, tangent, cotangent, secant, cosecant, cotangent. The basic angles which we consider while simplifying the functions begin from 00 to 900which we consider most of the time in Right Angle triangle. They are explained below in tabulation form here in the horizontal format values are there and in vertical format the angles are there:

 00 300 450 600 900 Sin C 0 ½ √2/2 √3/2 1 Cos C 1 √3/2 √2/2 ½ 0 Tan C 0 1/√3 1 √3 ∞

Now rest of the trigonometric ratios can be found with the help of sin, cos and tan functions because the remaining functions i.e. the cosecant ( cosec), secant (sec), cotangent (cot) are reciprocal function cosine (cos), sine (sin), tangent (tan).
Sec C = 1/ cos C,
Cosec C = 1/ sin C,
Cot C = 1/ tan C =cos C / sin C.

These definitions are also referred as the Ratio identities. Considering the Pythagorean trigonometric identity the basic relationship exist between the sin and cosine:
sin2 θ + cos2 θ = 1.
The equation can also be written as sin θ = √(1- cos2 θ) and cos θ = √( 1- sin2 θ
θ (pronounced as theta) is a Greek letter used here to represent the angle.

Coterminal Angles

An angle is defined as a figure or form. It is any shape formed by two lines or rays connected as a given end Point. The point in an angle where two rays meet is called to be a vertex. Angles are of different types:
ACUTE ANGLE: An angle that is less than 90 degree.
OBTUSE ANGLE: An angle that is more than 90 degree.
RIGHT ANGLE: An angle that is exactly 90 degree.

In mathematics, quadrant term is used for the “quarter". In a coordinate graph as shown below, the Intersection of the two axes creates four regions. These four regions are called quadrants. Usually they are named by Roman Numbers as I, II, III and IV.

In the first quadrant, both coordinates (x and y) are positive. (+,+)

Positive and Negative Angles

We come across the terms positive and negative angle, when we study about the Triangles in the Trigonometry. Word trigonometry is derived from the tri - go- no, which means the study of the sides and the angles of the three sided figures. So we say that the study of trigonometry is the science in which we study about the three sided figures and the formation...Read More

In mathematics, when two rays make a figure, which is called as an angle. In Geometry mathematics, an angle is a very important aspect.  Trigonometry is based on the measurement of an angle. There are two units which are used in measurement of an angle one is degree and other is radian.
Mostly we use the unit degree which is popular than radian. Further deg...Read More

Reference Angle

The term angle is mainly used in the Geometry and Trigonometry. When two rays make or form a figure then they also form an angle. Angle is used in measuring the rotation of any Ray with respect to some fix Point. When a ray inclines over a ray then the two rays form an angle. Angles are of various type, here we will discuss reference angle.
An Acute Angle, which is posi...Read More